ru.wikipedia.org website review
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ru.wikipedia.org is 50% geoptimaliseerd!
SEO Keyword summary for ru.wikipedia.org/wiki/%d0%a4%d0%b8%d0%b3%d1%83%d1%80%d0%bd%d1%8b%d0%b5_%d1%87%d0%b8%d1%81%d0%bb%d0%b0
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be displaystyle
Focus keyword
Short and long tail
Short Tail Keywords displaystyle frac oeis |
long Tail Keywords (2 words) ndisplaystyle n pnkdisplaystyle pnk kdisplaystyle k kdisplaystyle k- k- pnkdisplaystyle |
long Tail Keywords (3 words) k- pnkdisplaystyle pnk pnk ndisplaystyle n 1 k2displaystyle k-2 pnkdisplaystyle pnk ndisplaystyle pnkdisplaystyle pnk kdisplaystyle kdisplaystyle k kdisplaystyle n3n12textstyle frac n3n-12 |
ru.wikipedia.org On-Page SEO Scan
Descriptive Elements
The <head> element of a ru.wikipedia.org/wiki/%d0%a4%d0%b8%d0%b3%d1%83%d1%80%d0%bd%d1%8b%d0%b5_%d1%87%d0%b8%d1%81%d0%bb%d0%b0 page is used to inform the browser and visitors of the page about the general meta information. The head section of the page is where we place the page title, the definition of the HTML version used, the language of in which the page is written. In the head section we can also include JavaScript and CSS (markup) files for the page.
Page title
Title length
mdash
Meta description
Meta description legth
Meta description SEO
No meta relevance in the description detected !
Content SEO
Number of Words
Spam detected?
Headings
Heading distribution
Heading normalisation
Heading SEO impact
No headings were found !
Emphasis (bold and italic)
Emphasis SEO impact
Images
Number of images
Images dimensions
Image alt descriptions
Images SEO impact
displaystyle kgeqslant pnk dots textstyle pnknk frac pnkbegincases endcases pnkpn pnkspnks pnkfrac kfrac kdots pnkdots sfrac leftgamma psi right gamma tnpn tntn over sum infty left color blue black quad acbd adbc ldots sqrt equiv pmod nequiv npmod npnkfrac colon pnkk npnk nfrac kxp qquad xndots tfrac lefttfrac cos sin operatorname ktn tnn cnk fxfrac ckkpk kquad nkp nkfrac pnkn nkpi ntimes qnn qntn ngeqslant qnpi sndfrac qndnd beginarrayc red endarray catn catnsn nsn snm tnsn qndsum dsdmnn external links wikimedia foundation powered mediawiki
Mobile SEO ru.wikipedia.org/wiki/%d0%a4%d0%b8%d0%b3%d1%83%d1%80%d0%bd%d1%8b%d0%b5_%d1%87%d0%b8%d1%81%d0%bb%d0%b0
Mobile rendering
Mobile optimizations
Responsive design detected (mobile css)
No flash detected !
Mobile improvement
Marketing / lead generation for ru.wikipedia.org/wiki/%d0%a4%d0%b8%d0%b3%d1%83%d1%80%d0%bd%d1%8b%d0%b5_%d1%87%d0%b8%d1%81%d0%bb%d0%b0
Social Media
Facebook shares | Facebook likes | ||
Facebook comments | Tweets | ||
Google +1 |
Conversion form
Search form
Analytics
Online presence
SERP Preview
SERP Title
SERP Link
SERP Description
Domain Level SEO
Domain name
16 characters long
Domain name SEO Impact
Path name
No contextual keywords found in path
Structured data
Publisher Markup
Other Structured data
Website configuration
Correct processing of non-existing pages?
Favicon icon found?
Robots.txt found?
Sitemap found?
Navigation and internal links
Navigation
Url seperator
Human readable urls
Number of links
Link SEO Impact
creativecommons.org creative commons cc bysa
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oeis.org a000217
a000290
a000326
a001318
a000384
a051624
a001110
a014979
a046194
a036353
a046177
a036354
a046180
a048900
a48903
a062712
a000566
a000567
a001106
a244646
a001107
a051682
a051865
a051866
a051867
a051868
a051869
a051870
a051871
a051872
a051873
a195163
a167149
a005448
a125602
a001844
a027862
a005891
a145838
a003215
a002407
a069099
a144974
a144975
a060544
a062786
a090562
a128862
a133161
a102871
a129445
a006244
a031138
a087125
a006051
a001570
a001921
a000292
a027568
a003556
a000330
a000578
a018889
a039596
a060728
a039595
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ru.m.wikipedia.org |
w httpsruwikipediaorgwindexphptitleoldid135170084
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wiki 1
/%D0%93%D0%B0%D1%83%D1%81%D1%81,_%D0%9A%D0%B0%D1%80%D0%BB_%D0%A4%D1%80%D0%B8%D0%B4%D1%80%D0%B8%D1%85
1
1
1
1
20
mathworld
wayback machine
jstor
history of the theory of numbers
1
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wikimediafoundation.org wikimedia foundation inc
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Links to external pages
Outloing links
en.wikipedia.org
en.wikipedia.org
www.archive.org
www.archive.org
eqworld.ipmnet.ru
web.archive.org
ilib.mccme.ru
web.archive.org
mathworld.wolfram.com
www.math24.ru
web.archive.org
www.personal.psu.edu
www.jstor.org
books.google.ru
www.archive.org
ilib.mccme.ru
books.google.com
www.e-osnova.ru
mathworld.wolfram.com
mathworld.wolfram.com
www.wikidata.org
mathworld.wolfram.com
www.snl.no
ru.wikisource.org
www.d-nb.info
www.wikidata.org
commons.wikimedia.org
ar.wikipedia.org
ca.wikipedia.org
de.wikipedia.org
eml.wikipedia.org
en.wikipedia.org
eo.wikipedia.org
es.wikipedia.org
fi.wikipedia.org
fr.wikipedia.org
gl.wikipedia.org
hu.wikipedia.org
id.wikipedia.org
it.wikipedia.org
ja.wikipedia.org
nl.wikipedia.org
nn.wikipedia.org
no.wikipedia.org
pt.wikipedia.org
ro.wikipedia.org
sr.wikipedia.org
ta.wikipedia.org
zh.wikipedia.org
www.wikidata.org
foundation.wikimedia.org
developer.wikimedia.org
foundation.wikimedia.org
www.wikimediafoundation.org
SEO Advice for ru.wikipedia.org
In this section we provide pointers on how you can to optimize your web page so it can be found more easily by search engines and how to make it rank higher by optimizing the content of the page itself. For each of the individual criteria the maximum score is 100%. A score below 70% is considered to be indication that the page is not complying with general SEO standards and should be evaluated and/or fixed. Not every factor is weighted the same and some are not as important as others. Relatively unimportant factors like meta keywords are not included in the overall score.
Item | Factor | Pointers | |
---|---|---|---|
PageTitle | 100% | Far too many sites lack a page title. A page title is the first thing that shows in the search results so always use the title element. | |
Title relevance | 0% | A title should reflect the contents of a site. This site has a 0 % match | |
Title Length | 100% | Limit your title to anywhere between 40 and 70 characters. Your title was 55 characters long | |
Meta Description | 0% | A meta description is the second element that shows in the search results so always use the meta description. | |
Meta description length | 0% | The meta description should be between 145 and 160 characters. This meta description is 1 characters long. | |
Meta description relevance | 0% | Meta Description should reflect the contents of a site. This site has a 0 % match | |
Number of internal links | 30% | Linking to internal pages makes pages easier to find for search engines. Try to keep the number of links on your page roughly below 100. There are 515 internal links on this page. | |
Folder structure | 100% | We found a folder structure in the links on your page. A good folder structure makes a site easier to navigate. We found 6 level 1 folders and 9 folders above or in the first level of navigation. | |
Headings | 0% | Headers should reflect the contents of a site. This site has a 0 % match | |
Links | 34% | Link anchors should to some degree reflect the contents of a site. This site has a 17 % match | |
Image alt tags | 64% | Image alt tags should to some degree reflect the contents of a site. This site has a 23 % match | |
Bold and italic | 69% | Bold and italic tags should reflect the contents of a site to some degree. This site has a 23 % match | |
Html ratio | 30% | Try to keep the html / text ratio as low as possible. More html means longer loading times. Layout should be handled in a serpate css file | |
Image descriptions | 84% | 84.009546539379 % of all images have been described via the "alt" attribute. Describing images with relevant text may lead to better results in the search engines. | |
Page errors | 100% | Pages with no errors display significantly faster on most browsers. We detected 0 errors and warnings | |
WordCount | 20% | An ideal page contains between 400 and 600 words.This page contains 2778 words | |
Server response time | 100% | A fast server speeds up a website. This server responds 84.22% faster then average | |
Gzip compression | 30% | This site does not use Gzip compression. Pages may not display as fast as they could | |
Keywords in Domainname | 100% | There are important keywords in your domain name | |
Keywords in domain path | 20% | There are no important keywords in the domain path | |
Structured Data | 100% | Structured data makes it easier for search engines to index your website | |
Inline css | 0% | Do not use inline css declarations. Inline css will slow down the rendering of the website. We detected 795 inline style declarations ( <a style="color:green">) with a size of 28195 bytes | |
Excessive use of the same words | 100% | There is no indication that there are one or more keywords that are used excessively. | |
Frames or iframes | 100% | Perfect, detected not (i)frames on your webpagina | |
Flash | 100% | Perfect, we detected no flash objects on your page | |
Css | 30% | We detected too much (4) CSS files on your page. Css files block the loading of a webpage. | |
Javascript | 100% | Perfect, we did not detect too many blocking JavaScript files | |
Mobile Website | 100% | Perfect, we found a responsive design for mobile users | |
Most important heading | 100% | Perfect, we detected a correct use of the most important (h1) heading! | |
Normalized headings | 100% | Perfect, we found a correct use of normalized headings ! |
How would you like to have SEO advice for all your pages ?? Start your SEO Dashboard and optimize your website!
ru.wikipedia.org images and descriptions
265 images found at ru.wikipedia.org Images can improve the user experience for a website by making a pag visually appealing Images can also add extra keyword relevance to a webpage by using alt tags. Images can also slow down a website. If the width and height for a picture is not specified for a browser know in advance how large the image is. A browser must first load the picture and see before it knows how much space should be on the page. Upon reservation In the meantime, the browser can do little but wait. When the height and width for the plate are given in the HTML code, a browser just continues to build for a page while the images load in the background.
https://upload.wikimedia.org/wikipedia/commons/thumb/8/8b/small_skew_star_svg.svg/14px-small_skew_star_svg.svg.png height: 15 width: 14 description: Эта статья входит в число избранных |
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https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/the_sum_of_the_first_n_odd_integers_is_n%c2%b2._1%2b3%2b5%2b...%2b%282n-1%29%3dn%c2%b2..gif/220px-the_sum_of_the_first_n_odd_integers_is_n%c2%b2._1%2b3%2b5%2b...%2b%282n-1%29%3dn%c2%b2..gif height: 193 width: 220 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/a/ad/heptagonal_numbers.svg/220px-heptagonal_numbers.svg.png height: 215 width: 220 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40 height: height attribute not set width: width attribute not set description: {\displaystyle k} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0882ca78bf3c33c8ce7fe4ca00b03c1384babfe7 height: height attribute not set width: width attribute not set description: {\displaystyle k-2.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ab03963b958a4370995ed27175f011a1b5ec6608 height: height attribute not set width: width attribute not set description: {\displaystyle k\geqslant 3} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b height: height attribute not set width: width attribute not set description: {\displaystyle n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5cd3b36728dbb3a4bcc0d24748f56c67368b1f84 height: height attribute not set width: width attribute not set description: {\displaystyle p_{n}^{(k)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/44cdf5964b05432bc1d2465f426bcb018d18354d height: height attribute not set width: width attribute not set description: {\displaystyle 1+2+3+4\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dca02bde941e4eb5f5ef5bd052f9a64d2b9136bf height: height attribute not set width: width attribute not set description: {\displaystyle 1+3+5+7\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a4b5e44814a294afa508bd70e84724cbfa212c0b height: height attribute not set width: width attribute not set description: {\displaystyle 1,\;k,\;3k-3,\;6k-8,\;10k-15,\;15k-24,\;21k-35,\;28k-48,\;36k-63,\;45k-80\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/446e4c6fb13a41d15a3af43ac0877f0132bcaaec height: height attribute not set width: width attribute not set description: {\textstyle p_{n}^{(k)}=n+(k-2){\frac {n(n-1)}{2}}={\frac {(k-2)n^{2}-(k-4)n}{2}}={\frac {1}{2}}k(n^{2}-n)-n^{2}+2n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/25a8fe59e30a03ce1f0b79d2b476ac5c56ec9984 height: height attribute not set width: width attribute not set description: {\displaystyle 0,\;1,\;k,\;3k-3,\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d737860a91708914c2d66b5f923ddd5c33de22b1 height: height attribute not set width: width attribute not set description: {\displaystyle n=0.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a3cc3832bd788ded150eeca156c11a70e6880b2e height: height attribute not set width: width attribute not set description: {\displaystyle p_{n}^{(k)}={\begin{cases}1,&n=1\\p_{n-1}^{(k)}+(k-2)(n-1)+1,&n>1\end{cases}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4f88d60a1a331aa33aca69a968c8ed2653f22c70 height: height attribute not set width: width attribute not set description: {\displaystyle p_{n}^{(k+1)}=p_{n}^{(k)}+p_{n-1}^{(3)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ee74e1cc07e7041edf0fcbd4481f5cd32ad17b64 height: height attribute not set width: width attribute not set description: {\displaystyle n>1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/44e185ab9c990830d5055fa3ae698a4225ce67e0 height: height attribute not set width: width attribute not set description: {\displaystyle k,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8bb8d9d17fc586108b497ce4d465d6e46c7d15f2 height: height attribute not set width: width attribute not set description: {\displaystyle p_{n}^{(k+s)}+p_{n}^{(k-s)}=2p_{n}^{(k)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4437ddb40d0f251165177ef3f82788ee78238b6d height: height attribute not set width: width attribute not set description: {\displaystyle s=0,1,2\dots k-3} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c2d70c756eede0b37fcc81281dc1abdf6896810d height: height attribute not set width: width attribute not set description: {\textstyle p_{n}^{(k)}={\frac {2+(n-1)(k-2)}{2}}n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5b1cb69fc30fbcd3b77ac0013a51c30ac91da8ae height: height attribute not set width: width attribute not set description: {\displaystyle n>2.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/99862948fa9781aaa99ae2f88684c702791d760e height: height attribute not set width: width attribute not set description: {\textstyle {\frac {n}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b679192f0ebf7fef9ca330b9ae3178cbf94baaaa height: height attribute not set width: width attribute not set description: {\textstyle {\frac {2+(n-1)(k-2)}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2734765a623098e78ee5856f966ccb57b6f19a85 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{p_{1}^{(k)}}}+{\frac {1}{p_{2}^{(k)}}}+{\frac {1}{p_{3}^{(k)}}}+\dots +{\frac {1}{p_{n}^{(k)}}}+\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2 height: height attribute not set width: width attribute not set description: {\displaystyle s} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e1b0d8e70469430638b1e997d6c402e261a607aa height: height attribute not set width: width attribute not set description: {\textstyle s=-{\frac {2}{k-4}}\left(\gamma +\psi ({\frac {2}{k-2}})\right),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a height: height attribute not set width: width attribute not set description: {\displaystyle \gamma } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a596a1fb4130a47f6b88c66150497338bd6cbccc height: height attribute not set width: width attribute not set description: {\displaystyle \psi (x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf height: height attribute not set width: width attribute not set description: {\displaystyle 1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7fd591543c6ffeba17bb12075476c00165f54e9e height: height attribute not set width: width attribute not set description: {\displaystyle k-2} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/6/69/polygonal_number_3.gif/500px-polygonal_number_3.gif height: 77 width: 500 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/36688a2a9c1eb70db60203211854e8088cddd55a height: height attribute not set width: width attribute not set description: {\textstyle {\frac {n(n+1)}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3b6888bda6e6ba254e454de0f963f3fadbe69e4d height: height attribute not set width: width attribute not set description: {\textstyle t_{n}=p_{n}^{(3)}={\frac {n(n+1)}{2}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5fd1fe34fd2354a8577c9e5556a6d688f5a3ab6f height: height attribute not set width: width attribute not set description: {\displaystyle t_{2n}=3t_{n}+t_{n-1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a475c67d9c394222b022138a15cc423a0d6a2a91 height: height attribute not set width: width attribute not set description: {\displaystyle t_{2n+1}=3t_{n}+t_{n+1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/74b4ce689e5d250c9a9eb7154b7ba131e91b051d height: height attribute not set width: width attribute not set description: {\textstyle p_{n}^{(k)}=n+(k-2){\frac {n(n-1)}{2}}=(k-2)t_{n-1}+n=(k-3)t_{n-1}+t_{n}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/c/c3/square_number_16_as_sum_of_two_triangular_numbers.svg/200px-square_number_16_as_sum_of_two_triangular_numbers.svg.png height: 200 width: 200 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d8d937fdc77e4684d5a334d813ff1b622026b26a height: height attribute not set width: width attribute not set description: {\displaystyle t_{n}+t_{n+1}=(n+1)^{2}=p_{n+1}^{(4)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5b7a174e1658230b57624a80485eb4c5b4466e93 height: height attribute not set width: width attribute not set description: {\displaystyle s_{m-1}=1+3+6+\dots +{\frac {(m-1)m}{2}}={\frac {m^{3}-m}{6}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/70ba281e4598253e77474ec7e03507c2c1dc1c59 height: height attribute not set width: width attribute not set description: {\displaystyle 1+{1 \over 3}+{1 \over 6}+{1 \over 10}+{1 \over 15}+\dots =2\sum _{n=1}^{\infty }\left({1 \over n}-{1 \over n+1}\right)=2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3 height: height attribute not set width: width attribute not set description: {\displaystyle n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0871ecee561e6e5184e5d7586db657e6ad4ba59f height: height attribute not set width: width attribute not set description: {\displaystyle 8n+1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/48ede5c1dad0a2ecb89f3a98c5a110d444054e37 height: height attribute not set width: width attribute not set description: {\displaystyle 666=15^{2}+21^{2}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/9/91/square_number_1_with_gnomon.svg/24px-square_number_1_with_gnomon.svg.png height: 24 width: 24 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/d/d2/square_number_4_with_gnomon.svg/48px-square_number_4_with_gnomon.svg.png height: 48 width: 48 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/5/5b/square_number_9_with_gnomon.svg/70px-square_number_9_with_gnomon.svg.png height: 70 width: 70 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/4/41/square_number_16_with_gnomon.svg/92px-square_number_16_with_gnomon.svg.png height: 92 width: 92 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/81108220a10f82cd3b65b776d916cf99d5177a95 height: height attribute not set width: width attribute not set description: {\displaystyle 0+\color {blue}1\color {black}=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ecb1ac38f2397f4871bf565c9fa6fe7ef2fc2768 height: height attribute not set width: width attribute not set description: {\displaystyle 1+\color {blue}3\color {black}=4} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/51a80a65aaccf020a92a030c493bcbdb148d9234 height: height attribute not set width: width attribute not set description: {\displaystyle 4+\color {blue}5\color {black}=9} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4ebb3bcc228201ee16264eb372dd2d6321e7f521 height: height attribute not set width: width attribute not set description: {\displaystyle 9+\color {blue}7\color {black}=16} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ac9810bbdafe4a6a8061338db0f74e25b7952620 height: height attribute not set width: width attribute not set description: {\displaystyle n^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3f9eba0636d0b5bd752c7392e5e70ee0cd8021c2 height: height attribute not set width: width attribute not set description: {\displaystyle n^{2}=t_{n-1}+t_{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9f272c15b61a26fa952e293aab62ef0b9ad3baed height: height attribute not set width: width attribute not set description: {\displaystyle 4=1+3;\quad 9=3+6;\quad 16=6+10} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1c94a8bcb400c24056f5c8bd1d40a1f918be4e77 height: height attribute not set width: width attribute not set description: {\displaystyle n^{2}+t_{n-1}=p_{n}^{(5)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bce5c45fae5b02983395f63f80d89e0c6efdd803 height: height attribute not set width: width attribute not set description: {\textstyle 1^{2}+2^{2}+3^{2}+...+n^{2}={\frac {n(n+1)(2n+1)}{6}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fc4aefeb41365d26bc9575a4f31f02535ebb4247 height: height attribute not set width: width attribute not set description: {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+\dots +{\frac {1}{n^{2}}}+\dots ={\frac {\pi ^{2}}{6}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3114bc33cd78a0887bf8d10815aef9887438731f height: height attribute not set width: width attribute not set description: {\displaystyle (a^{2}+b^{2})(c^{2}+d^{2})=(ac-bd)^{2}+(ad+bc)^{2}=(ac+bd)^{2}+(ad-bc)^{2}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f1f73b8db768350c7fbcca48d374026de26bc08b height: height attribute not set width: width attribute not set description: {\displaystyle (1^{2}+4^{2})(2^{2}+7^{2})=26^{2}+15^{2}=30^{2}+1^{2}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/b/b5/pentagonal_number.gif/150px-pentagonal_number.gif height: 165 width: 150 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bc4657b6129bba9b10482101bab31e9cef66435d height: height attribute not set width: width attribute not set description: {\textstyle {\frac {n(3n-1)}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/675b5d9cbb43346347ea091bc02c1e8b12b6fe9d height: height attribute not set width: width attribute not set description: {\displaystyle p_{n}^{(5)}={\frac {n(3n-1)}{2}}=t_{n-1}+n^{2}=t_{n}+2t_{n-1}=t_{2n-1}-t_{n-1}={\frac {1}{3}}t_{3n-1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/df428a096d728c0816b917ff077438fb085b36a2 height: height attribute not set width: width attribute not set description: {\displaystyle p_{n}^{(5)}=n^{2}+t_{n-1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/217daf7c7c9747106ffbd0572c2adc4cf9e68b63 height: height attribute not set width: width attribute not set description: {\displaystyle n=0,\;1,\;-1,\;2,\;-2,\;3,\;-3\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5aba65522ae4a867eb184297b9037591ea2484ab height: height attribute not set width: width attribute not set description: {\displaystyle (1-x)(1-x^{2})(1-x^{3})\ldots =1-x-x^{2}+x^{5}+x^{7}-x^{12}-x^{15}+x^{22}+x^{26}-x^{35}-x^{40}+\ldots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4 height: height attribute not set width: width attribute not set description: {\displaystyle x} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/f/f0/hexagonal_numbers.svg/610px-hexagonal_numbers.svg.png height: 222 width: 610 description: Первые четыре шестиугольных числа. |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1df21ba96dbea095083a497a6c3617a40e103ea1 height: height attribute not set width: width attribute not set description: {\displaystyle 2n^{2}-n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b0719dca63588de04f3f997aea7b59b3a77cc88e height: height attribute not set width: width attribute not set description: {\displaystyle p_{n}^{(6)}=p_{2n-1}^{(3)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6073d10259562e9820c75194d24eaa364499aa43 height: height attribute not set width: width attribute not set description: {\textstyle {\frac {{\sqrt {8n+1}}+1}{4}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/07c6e121ec583da0bc76f9a34f1086808fddf9c1 height: height attribute not set width: width attribute not set description: {\displaystyle 5n^{2}-4n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/79992ac2766c324513320fc9960f4d390f4af571 height: height attribute not set width: width attribute not set description: {\displaystyle 5n(n-1)\equiv 0{\pmod {10}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3e05a4cfe93aa562e536d6121172a674dc1ff2b6 height: height attribute not set width: width attribute not set description: {\displaystyle 5n^{2}-4n\equiv n{\pmod {10}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/69581f726ee98c603fa74d330d7aeba8ac571075 height: height attribute not set width: width attribute not set description: {\displaystyle n>2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0e7279553bce4f68ee1310e3a0295de0699cd76a height: height attribute not set width: width attribute not set description: {\displaystyle n=p_{n}^{(k)}={\frac {(k-2)n^{2}-(k-4)n}{2}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/640fe0a054938c393e9add933d7a67f349ed2709 height: height attribute not set width: width attribute not set description: {\displaystyle 2n-2n=(k-2)(n^{2}-n)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/93bff947a8bbbf831b7ca93f31668a246ff7dcf4 height: height attribute not set width: width attribute not set description: {\displaystyle k-2={\frac {2n-2}{n-1}}-{\frac {2n}{n}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/015875334ac1fb4d67438b8f65f8407efef70ba6 height: height attribute not set width: width attribute not set description: {\displaystyle 2n-2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fbd0b0f32b28f51962943ee9ede4fb34198a2521 height: height attribute not set width: width attribute not set description: {\displaystyle n-1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/eacbd5b0e609e1f3d7da751ac0d50113d27d22aa height: height attribute not set width: width attribute not set description: {\displaystyle 2n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1ab579716c8ecd1c661faf3ed8c83c9f79de269f height: height attribute not set width: width attribute not set description: {\textstyle k={\frac {2n-2}{n-1}}-{\frac {2n}{n}}+2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/096452569622e6aa15847850a9bcce3f76f18628 height: height attribute not set width: width attribute not set description: {\displaystyle (n,\;k)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2f320d85d1b7ce6fc3d0f018e5b8a774d8984f65 height: height attribute not set width: width attribute not set description: {\displaystyle k<3} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0c03fdd723832bca266b9092f7a728b03bbaee90 height: height attribute not set width: width attribute not set description: {\displaystyle n=105} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cb748dd0d99ae5edb7a31fbb073fe28812df29d8 height: height attribute not set width: width attribute not set description: {\displaystyle 2n=210\colon \quad 1,\;2,\;3,\;5,\;6,\;7,\;10,\;14,\;15,\;21,\;30,\;35,\;42,\;70,\;105,\;210} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ee025bc2df3a7a9a00d37085d8b0f106d37c8ff9 height: height attribute not set width: width attribute not set description: {\displaystyle 2n-2=208\colon \quad 1,\;2,\;4,\;8,\;13,\;16,\;26,\;52,\;104,\;208} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9e0941053b827c2a5cd684a21d4f07ee31d15405 height: height attribute not set width: width attribute not set description: {\displaystyle n=2,\;3,\;5,\;14,\;105} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c8afac57f5c4d69847829c5de174fde4603fc9d0 height: height attribute not set width: width attribute not set description: {\displaystyle k=105,\;36,\;12,\;14,\;2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f98a943fc8154cb33675cf12be3131c686b2e399 height: height attribute not set width: width attribute not set description: {\displaystyle 105} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c6c18bc39b4b5f53857416d6b9c00f2231742adb height: height attribute not set width: width attribute not set description: {\displaystyle p_{2}^{(105)},\;p_{3}^{(36)},\;p_{5}^{(12)},\;p_{14}^{(14)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8716f1daf1eec1240a94195c93221d94eb420148 height: height attribute not set width: width attribute not set description: {\displaystyle n>2,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/90e0223fbf0516903379cc0e36637ecc9ba6f7ee height: height attribute not set width: width attribute not set description: {\displaystyle 8(k-2)p_{n}^{(k)}+(k-4)^{2}=(2n(k-2)-(k-4))^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/27e6b34ab3c7df55e3dc5a2fbc3bbb6505a0de71 height: height attribute not set width: width attribute not set description: {\displaystyle n=p_{n}^{(k)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/397bfafc701afdf14c2743278a097f6f2957eabb height: height attribute not set width: width attribute not set description: {\displaystyle n,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cb9a132a5e15d2e7ff939b82e9d3806e48e9ab48 height: height attribute not set width: width attribute not set description: {\displaystyle 8(k-2)n+(k-4)^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5ce07e278be3e058a6303de8359f8b4a4288264a height: height attribute not set width: width attribute not set description: {\displaystyle r^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f85a165d0f1976a74895d9c4669bcf2bb8591a60 height: height attribute not set width: width attribute not set description: {\textstyle n={\frac {r+k-4}{2k-4}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e87ce11d2c9019bb09c9857c7e971b733956f7aa height: height attribute not set width: width attribute not set description: {\displaystyle 1540} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/94aaaddc347cb5c5159d0bcc22c6971bddc94951 height: height attribute not set width: width attribute not set description: {\displaystyle 98596=314^{2},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1a8d4d3e04e2cdf33d41a5a1c144966267e35aed height: height attribute not set width: width attribute not set description: {\displaystyle n=20,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2f9498d60b2319a4ae7c5607794b537c559a976d height: height attribute not set width: width attribute not set description: {\displaystyle |x|<1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2a03f2ed977551c13f8900f447807f5f09b1aed7 height: height attribute not set width: width attribute not set description: {\textstyle p_{1}^{(k)}x+p_{2}^{(k)}x^{2}+p_{3}^{(k)}x^{3}+\dots ={\frac {x(1+(k-3)x)}{(1-x)^{3}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/662e06a2436f8a44fec791f5c794621f10dc8f30 height: height attribute not set width: width attribute not set description: {\displaystyle k=3} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e7398724a0c2e81af6135a014ae54bb3138bbf3b height: height attribute not set width: width attribute not set description: {\textstyle \qquad {\frac {x}{(1-x)^{3}}}=p_{1}^{(3)}x+p_{2}^{(3)}x^{2}+p_{3}^{(3)}x^{3}+\dots +p_{n}^{(3)}x^{n}+\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b96ee1f0df5aee064133a126f203a7d84e50e19b height: height attribute not set width: width attribute not set description: {\displaystyle k=4} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9247fbb07ae9f4f44e45495da9839a8c1ab315f5 height: height attribute not set width: width attribute not set description: {\textstyle \qquad {\frac {x(x+1)}{(1-x)^{3}}}=p_{1}^{(4)}x+p_{2}^{(4)}x^{2}+p_{3}^{(4)}x^{3}+\dots +p_{n}^{(4)}x^{n}+\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bcf68fa52735a07a4e91b5735726a88f79bee969 height: height attribute not set width: width attribute not set description: {\displaystyle k=5} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3127ba8fbcc55fb7760926d1a793bf0fc17afe3d height: height attribute not set width: width attribute not set description: {\textstyle \qquad {\frac {x(2x+1)}{(1-x)^{3}}}=p_{1}^{(5)}x+p_{2}^{(5)}x^{2}+p_{3}^{(5)}x^{3}+\dots +p_{n}^{(5)}x^{n}+\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2726e58583584ac45ba80452f8718ae8db8da9c9 height: height attribute not set width: width attribute not set description: {\displaystyle 1,\;36,\;1225,\;41616,\;1413721\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0bce8619ef4c0d40858e2cae6b01f5dcb472b492 height: height attribute not set width: width attribute not set description: {\textstyle {\frac {x(1+x)}{(1-x)(1-34x+x^{2})}}=x+36x^{2}+1225x^{3}+\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9135395a44c1f2acd287b156a732cd3357c52447 height: height attribute not set width: width attribute not set description: {\displaystyle |x|<17-12{\sqrt {2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/09bc55b65d25794c1ed9d8b62aec12c1ae15aaa0 height: height attribute not set width: width attribute not set description: {\displaystyle 10^{22166},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d7e855dbac30eaed65afe91e3b6f9e6f021a013a height: height attribute not set width: width attribute not set description: {\displaystyle p_{5}^{(12)},\;p_{14}^{(14)},\;p_{3}^{(36)},\;p_{2}^{(105)}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a height: height attribute not set width: width attribute not set description: {\displaystyle \pi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/65bf94f4ed88baee37f729cf3a9e7e8783d52fe5 height: height attribute not set width: width attribute not set description: {\displaystyle 3\ln 3-{\frac {\pi {\sqrt {3}}}{3}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/70dd540833a8bb66b34d16a17aa3f617f522c548 height: height attribute not set width: width attribute not set description: {\displaystyle {\tfrac {\pi }{3}}{\sqrt {1-{\tfrac {2}{\sqrt {5}}}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5e1e3917e0120154366e54a488f99925025cb696 height: height attribute not set width: width attribute not set description: {\displaystyle +{\tfrac {5}{6}}\ln 5-{\tfrac {\sqrt {5}}{3}}\ln \left({\tfrac {1+{\sqrt {5}}}{2}}\right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1519618d15b1d7b57403f53104ab44b81bfb2f85 height: height attribute not set width: width attribute not set description: {\displaystyle {\tfrac {1}{5}}(2\ln 14+4\cos {\tfrac {\pi }{7}}\ln \cos {\tfrac {3\pi }{14}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/267706da9c4f7533a9d4724ff065fb5055534862 height: height attribute not set width: width attribute not set description: {\displaystyle +\ln \sin {\tfrac {\pi }{7}}\sin {\tfrac {\pi }{14}}-\ln \cos {\tfrac {\pi }{14}}\sin {\tfrac {3\pi }{14}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/51d00088cc7386375af0b8bde55e56c0d47fefe6 height: height attribute not set width: width attribute not set description: {\displaystyle +\pi \operatorname {tg} {\tfrac {3\pi }{14}})} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/c/c5/centered_triangular_number_19.svg/120px-centered_triangular_number_19.svg.png height: 104 width: 120 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/5/5c/centered_square_number_25.svg/120px-centered_square_number_25.svg.png height: 120 width: 120 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/9/94/centered_pentagonal_number_31.svg/120px-centered_pentagonal_number_31.svg.png height: 114 width: 120 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/8/88/hex_number_37.svg/120px-hex_number_37.svg.png height: 137 width: 120 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a7248c43da3b5143eefaf6b1fb536c6756bb5f8d height: height attribute not set width: width attribute not set description: {\displaystyle 1+k+2k+3k+4k+\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f620ee43bf237508d63d92939bac6644dd56e6a6 height: height attribute not set width: width attribute not set description: {\displaystyle k=4,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2aade34f9590e3cb681f819c4a36995a603b470c height: height attribute not set width: width attribute not set description: {\displaystyle 1,5,13,25,41\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fe0bda09daf55a7bfc8718e1a54c0174e33602b7 height: height attribute not set width: width attribute not set description: {\displaystyle 1+k(1+2+3+4+\dots )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9b43bcd14cd49c7e32ad04ebfcb40e6436fe0d4f height: height attribute not set width: width attribute not set description: {\displaystyle kt_{n-1}+1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4ade4950f2f3a04a5ec09a8ed299482d7a298e20 height: height attribute not set width: width attribute not set description: {\displaystyle t_{n}~(n=1,\;2,\;3\dots )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/52572c0ded1c137cf074c014b01529457c672b63 height: height attribute not set width: width attribute not set description: {\displaystyle 1+4+8+12\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1b8100d23ed20b0500b3c909c27d887c9d66ecf1 height: height attribute not set width: width attribute not set description: {\displaystyle c_{n}^{(k)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/36d4fc6bf9cba0dd852d896de1631f1593fd1dd4 height: height attribute not set width: width attribute not set description: {\textstyle c_{n}^{(k)}=1+k{\frac {n(n-1)}{2}}={\frac {kn^{2}-kn+2}{2}};\ n=1,\;2,\;3\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5e63748bc141ac1720e497e9c2193fbcb55b172f height: height attribute not set width: width attribute not set description: {\textstyle f(x)={\frac {x(1+(k-2)x+x^{2})}{(1-x)^{3}}};\quad |x|<1} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/c/c5/centered_triangular_number_19.svg/220px-centered_triangular_number_19.svg.png height: 191 width: 220 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d138165a900174526ab300947f3fdd6927aa0a66 height: height attribute not set width: width attribute not set description: {\textstyle c_{n}^{(3)}={\frac {3n^{2}-3n+2}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d68ff64872d5060e7ae21e602512d31c85c6f9e7 height: height attribute not set width: width attribute not set description: {\textstyle c_{n}^{(3)}=3t_{n-1}+1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/feefb2f1a15d3fd7faa301078a870b3a859c00fe height: height attribute not set width: width attribute not set description: {\textstyle {\frac {3n^{2}-3n+2}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/572b3f47a4582336a3128fddb962eaff38bd2a43 height: height attribute not set width: width attribute not set description: {\displaystyle c_{n}^{(3)}=p_{n}^{(3)}+p_{n-1}^{(3)}+p_{n-2}^{(3)}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/286177b5be9da944e6467e964f54cf0d068ba27a height: height attribute not set width: width attribute not set description: {\displaystyle c_{n}^{(3)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1d4bb2662bd4951087d40e217559205971339e54 height: height attribute not set width: width attribute not set description: {\displaystyle t_{n-1}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/e/ec/reddot.svg/16px-reddot.svg.png height: 16 width: 16 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/f/fe/graydot.svg/16px-graydot.svg.png height: 16 width: 16 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/15912dca7ccee4dcb83a509dcf8679c22866d6c9 height: height attribute not set width: width attribute not set description: {\textstyle c_{n}^{(4)}={(2n-1)^{2}+1 \over 2}=2n^{2}-2n+1=(n-1)^{2}+n^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/95059fe2dc0dcac27ac9c3ef527c1820263e5d0c height: height attribute not set width: width attribute not set description: {\displaystyle n^{2}+(n-1)^{2}\dots } |
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https://upload.wikimedia.org/wikipedia/commons/thumb/9/94/centered_pentagonal_number_31.svg/220px-centered_pentagonal_number_31.svg.png height: 210 width: 220 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/80498ce978d7fd4b374ec88030d453b0f687b226 height: height attribute not set width: width attribute not set description: {\textstyle c_{n}^{(5)}={\frac {5(n-1)^{2}+5(n-1)+2}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/68009ca1adf15f95fc525ddce1530576c6171bc2 height: height attribute not set width: width attribute not set description: {\textstyle {\frac {5(n-1)^{2}+5(n-1)+2}{2}}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/centered_hexagonal_%3d_1_%2b_6triangular.svg/200px-centered_hexagonal_%3d_1_%2b_6triangular.svg.png height: 172 width: 200 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3737d34bf6801a3ca185c4165d9774726118a052 height: height attribute not set width: width attribute not set description: {\textstyle 1+{\frac {6(n(n-1)}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/df88c6333caaf6471cf277f24b802ff9931b133e height: height attribute not set width: width attribute not set description: {\displaystyle (n-1)} |
|
https://wikimedia.org/api/rest_v1/media/math/render/svg/ab9d1c5b5a04f751c783a3b8e62f99e1799c10e9 height: height attribute not set width: width attribute not set description: {\displaystyle c_{n}^{(6)}=n^{3}-(n-1)^{3}=3n(n-1)+1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c855d80b59acf7d06f5657921c034423d48a225a height: height attribute not set width: width attribute not set description: {\displaystyle 1+3n(n-1)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3e9d1a52e455a7a5272a345b2697e35f1579b681 height: height attribute not set width: width attribute not set description: {\displaystyle n^{3}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4f282cafa713927c52bdd5ebb7ea3c3314c68813 height: height attribute not set width: width attribute not set description: {\displaystyle c_{n}^{(6)}=2c_{n-1}^{(6)}-c_{n-2}^{(6)}+6} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/1/13/centered_heptagonal_number.svg/240px-centered_heptagonal_number.svg.png height: 240 width: 240 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7ab5bc95596798d9f6707806cd0dd4e33ac2e5ca height: height attribute not set width: width attribute not set description: {\textstyle {\frac {7n^{2}-7n+2}{2}}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/centered_octagonal_number.svg/280px-centered_octagonal_number.svg.png height: 280 width: 280 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/997a2e07301fde684b2ccbce6d203233c0c290b1 height: height attribute not set width: width attribute not set description: {\displaystyle (2n-1)^{2}=4n^{2}-4n+1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c18f7af77d7fef65fe7850bead6cdc34382503f8 height: height attribute not set width: width attribute not set description: {\displaystyle c_{n}^{(6)}=p_{2n-1}^{(4)}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/30af7fc89857e51f4bc2c9880cdc7c149c8929dc height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {(3n-2)(3n-1)}{2}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3173c295f3fb8c28c4aa881465f5cc0b6fb1595f height: height attribute not set width: width attribute not set description: {\displaystyle c_{n}^{(9)}=p_{3n-2}^{(3)}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/7/70/centered_nonagonal_number.svg/280px-centered_nonagonal_number.svg.png height: 280 width: 280 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1f1ae2e3a072775bced4e36566f960b3f0ea61fc height: height attribute not set width: width attribute not set description: {\displaystyle 5(n^{2}-n)+1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d37c40366a871cf3aeac8f4cc53cd2c4654f22b9 height: height attribute not set width: width attribute not set description: {\displaystyle 1,\;10,\;25,\;51} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/22ff02193de392ecc3a6b169d57e2d0382be499f height: height attribute not set width: width attribute not set description: {\displaystyle c_{k}^{(k)}=p_{k+1}^{(k)}\quad } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bcb6778a29f576eb23da1dbddffb73b2571359ac height: height attribute not set width: width attribute not set description: {\displaystyle k.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e392efc678bd62a47b3e18a38b8ab60f73e935f5 height: height attribute not set width: width attribute not set description: {\displaystyle 1,\;10,\;136,\;1891,\;26335\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/17d19658b826432c4334c3d0e14cc10e9615c60a height: height attribute not set width: width attribute not set description: {\displaystyle m^{2}+m=3n^{2}-3n+2,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5d9e5fe70a38a5d98fa54c7c8b8a5d86ef3500c1 height: height attribute not set width: width attribute not set description: {\displaystyle p_{m}^{(3)}=c_{n}^{(3)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9b804a0b07e90b9806985517eff2ba66ccf467a5 height: height attribute not set width: width attribute not set description: {\displaystyle m=1,\;4,\;16,\;61,\;229\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e70129762ee6b1d73f5b6cb63a158ae03bbf2989 height: height attribute not set width: width attribute not set description: {\displaystyle n=1,\;3,\;10,\;36,\;133\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ed63ab257e03e755b6abe75430d92b4b8a35b39a height: height attribute not set width: width attribute not set description: {\textstyle m^{2}={\frac {3n^{2}-3n+2}{2}}.\quad } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/80648a66bbdceece367c10a10793edbb220f33d7 height: height attribute not set width: width attribute not set description: {\displaystyle c_{m}^{(3)}=p_{n}^{(4)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d5d80d276aed7641d4c9afea1a25b1eb0775de2a height: height attribute not set width: width attribute not set description: {\displaystyle m=1,\;2,\;8,\;19,\;79\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0799b6bfa6fc01716bceb85b840162aaa271b038 height: height attribute not set width: width attribute not set description: {\displaystyle n=1,2,7,16,65\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5a636fb5465fac9a89de68855d0f79adff62ad80 height: height attribute not set width: width attribute not set description: {\displaystyle 1,\;4,\;64,\;361,\;6241\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/72c527a2159a4815026eccd580f1b4a922ccc011 height: height attribute not set width: width attribute not set description: {\displaystyle 1,\;91,\;8911,\;873181,\;85562821\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0e0eae92b60a578ee6f20ba585b428b618a2c224 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {m(m+1)}{2}}=3n^{2}+3n+1.\quad } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8303eb638ccdf825aef5a97b88557264eea3afdc height: height attribute not set width: width attribute not set description: {\displaystyle p_{m}^{(3)}=c_{n+1}^{(6)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6075ff22d7fffd0e77505581f16dc8fe6ce004e9 height: height attribute not set width: width attribute not set description: {\displaystyle m=1,13,133,1321,13081\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9ecb06ccbb5a33f5b48ef140cbd8aa3478fbb3ef height: height attribute not set width: width attribute not set description: {\displaystyle n=0,\;5,\;54,\;539,\;5340\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9a5fa27bc8eac542519553a20e19612f51bc6586 height: height attribute not set width: width attribute not set description: {\displaystyle 1,\;169,\;32761,\;6355441,\;1232922769\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/84355261959f1c9d7f871832466b2f76c5eade12 height: height attribute not set width: width attribute not set description: {\displaystyle m^{2}=3n^{2}+3n+1.\quad } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6a3bb2bb260a55e2aa83aac9f180399b082771c1 height: height attribute not set width: width attribute not set description: {\displaystyle p_{m}^{(4)}=c_{n+1}^{(6)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8f741771912972202f69dffe7a2fef45cf525271 height: height attribute not set width: width attribute not set description: {\displaystyle m=1,\;13,\;181,\;2521,\;35113\dots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bdb5472fdf39ff2ef71003feaa305c6ed76853d8 height: height attribute not set width: width attribute not set description: {\displaystyle n=0,\;7,\;104,\;1455,\;20272\dots } |
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https://upload.wikimedia.org/wikipedia/commons/thumb/4/47/square_pyramidal_number.svg/360px-square_pyramidal_number.svg.png height: 175 width: 360 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2627545022c95c5a6a4cb82881e5977edd7dbf55 height: height attribute not set width: width attribute not set description: {\displaystyle \pi _{4}^{(4)}=1+4+9+16=30} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c5d06101ae79e4d56f9d2c67ef26e4084741bbf9 height: height attribute not set width: width attribute not set description: {\displaystyle \pi _{n}^{(k)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f2fc10f2142acc76b6505d5cd3dee57e2200cadf height: height attribute not set width: width attribute not set description: {\displaystyle \pi _{n}^{(k)}=p_{1}^{(k)}+p_{2}^{(k)}+p_{3}^{(k)}+\dots +p_{n}^{(k)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/95e55c89b5a9d104c23645e0943bf2d7b7687470 height: height attribute not set width: width attribute not set description: {\displaystyle \pi _{n}^{(k)}={\frac {n(n+1)((k-2)n-k+5)}{6}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b5ba6bedd355e0fec63bd9ade6b93bf67962febd height: height attribute not set width: width attribute not set description: {\displaystyle \pi _{n}^{(k)}={\frac {(k-2)n-k+5}{3}}p_{n}^{(3)}={\frac {n+1}{6}}(2p_{n}^{(k)}+n)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/54d58fbcd542c1eb8ea71a2d3f4d8382442a10f9 height: height attribute not set width: width attribute not set description: {\displaystyle \pi _{n}^{(k+1)}=\pi _{n}^{(k)}+\pi _{n-1}^{(3)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5f9991591d9d4c8855e5c9499d8fcd347f4ba12f height: height attribute not set width: width attribute not set description: {\displaystyle f(x)={\frac {x(1+(k-3)x)}{(1-x)^{4}}};\quad |x|<1} |
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https://upload.wikimedia.org/wikipedia/commons/d/d5/pyramid_of_35_spheres_animation.gif height: 120 width: 160 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2d64b24ac9a5c67ef8e3ae80f109ce6e325d8464 height: height attribute not set width: width attribute not set description: {\displaystyle n-} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c2cd4e3f289b539111a52b3cd05f0d7f41007ac4 height: height attribute not set width: width attribute not set description: {\displaystyle \pi _{n}^{(3)}=t_{1}+t_{2}+\dots +t_{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6e0be322a4df9f7166b81617e4e247bcfb2bcd04 height: height attribute not set width: width attribute not set description: {\displaystyle \pi _{n}^{(3)}={\frac {n(n+1)(n+2)}{6}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2ca703fc138066957a4cf63aaa47e28e7222bb07 height: height attribute not set width: width attribute not set description: {\displaystyle \pi _{n}^{(k)}=\pi _{n}^{(3)}+(k-3)\pi _{n-1}^{(3)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fe56b7b4e734807a58e2b652343c06252fe8e736 height: height attribute not set width: width attribute not set description: {\displaystyle 1^{2}=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/544566e539538b9b5d5f9106712550b2c80da685 height: height attribute not set width: width attribute not set description: {\displaystyle 2^{2}=4} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b5875fac61d097be06efbab3e17b81d49db049ad height: height attribute not set width: width attribute not set description: {\displaystyle 140^{2}=19\,600} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/14b16b205b80c97fe123a37a365e9712769e148c height: height attribute not set width: width attribute not set description: {\displaystyle \pi _{n}^{(4)}={\frac {n(n+1)(2n+1)}{6}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/759a0962620483ce31bc4598377927ee3d41602e height: height attribute not set width: width attribute not set description: {\displaystyle \pi _{n}^{(4)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/59d2b4cb72e304526cf5b5887147729ea259da78 height: height attribute not set width: width attribute not set description: {\displaystyle n\times n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/25ebdedc645848c174183b686fa842fdc519363b height: height attribute not set width: width attribute not set description: {\displaystyle 4\pi _{n}^{(4)}=\pi _{2n}^{(3)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/91abd202f36a456dae1a5ae6752ce6143676b87f height: height attribute not set width: width attribute not set description: {\displaystyle \pi _{n}^{(4)}=\pi _{n}^{(3)}+\pi _{n-1}^{(3)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b66665c413238b1da37c1cb97c59bf2a91c23253 height: height attribute not set width: width attribute not set description: {\displaystyle q_{n}=n^{3},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/503d0af3998f76cd4eaf8b3cc5e8834e254cb71b height: height attribute not set width: width attribute not set description: {\displaystyle q_{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5cc583f192fd54cb2b3e4c5458c1e0d9bc44a086 height: height attribute not set width: width attribute not set description: {\displaystyle q_{n}=n^{3}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bc8c1ddde4258098af005bacfcbe69256a938f13 height: height attribute not set width: width attribute not set description: {\displaystyle q_{n}=(t_{n})^{2}-(t_{n-1})^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5fc9296c4967806b9a64fb5384a0b8f93d5ddf4c height: height attribute not set width: width attribute not set description: {\displaystyle n\geqslant 2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/04c1f27f13b70ddc9f3a2eae774eb194e19de1e6 height: height attribute not set width: width attribute not set description: {\displaystyle q_{1}+q_{2}+q_{3}+\dots +q_{n}=(t_{n})^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f6ed391b4d3efa1b934c4b4d23bb310c167958b0 height: height attribute not set width: width attribute not set description: {\displaystyle q_{n}=\pi _{n}^{(3)}+4\pi _{n-1}^{(3)}+\pi _{n-2}^{(3)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/44e71ac55b9fbf1e9f341b946cda63d61d3ef2cd height: height attribute not set width: width attribute not set description: {\displaystyle n>2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/256b37bc3ac27bbe416af5e0bbf2a22897f518fc height: height attribute not set width: width attribute not set description: {\displaystyle f(x)={\frac {x(x^{2}+4x+1)}{(x-1)^{4}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab height: height attribute not set width: width attribute not set description: {\displaystyle d} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/28a47962c7f0baec91883adc82aeda56e4695839 height: height attribute not set width: width attribute not set description: {\displaystyle s_{n}^{[d]}={\frac {(n-1+d)!}{(n-1)!\ d!}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/75baa5e8e4f48950b9f95e7ea0835c86332aead5 height: height attribute not set width: width attribute not set description: {\displaystyle s_{n}^{[2]}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f84359e60c6739fcab45e20313d1a9c15fb08fd1 height: height attribute not set width: width attribute not set description: {\displaystyle s_{n}^{[3]}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d44ef89cadef001a85fd17138679ec391a436e2d height: height attribute not set width: width attribute not set description: {\displaystyle s_{n}^{[4]}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/994da48a0b29edfff10ede51a2387ff370b62a11 height: height attribute not set width: width attribute not set description: {\displaystyle q_{n}^{[d]}=n^{d}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/430afef0270143f5d043597cc34f4216553e3e07 height: height attribute not set width: width attribute not set description: {\displaystyle (d=4)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c990e8a24517252e76f85ebd49eadcef4a644d8f height: height attribute not set width: width attribute not set description: {\displaystyle 1,10,120,1540,7140} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/65a234d89acfb1d8d2f9bf1d0948af21dc4a8f01 height: height attribute not set width: width attribute not set description: {\displaystyle 1,55,91,208335} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6bad91c8e9e42dd4c42708cb739eefcba254f72b height: height attribute not set width: width attribute not set description: {\displaystyle 1,4,19600} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/162e71a293d698c7d2d2538fd57b6d0903af3f49 height: height attribute not set width: width attribute not set description: {\displaystyle 1,4900} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d3fdd29d6162d7057fddd034ef08709794e9cae9 height: height attribute not set width: width attribute not set description: {\displaystyle n(n+1),n\geqslant 0.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc height: height attribute not set width: width attribute not set description: {\displaystyle a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3 height: height attribute not set width: width attribute not set description: {\displaystyle b} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/24d87ad42152921d1e9e75b658994d08fdf76d5f height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{c}1\\1\quad 1\\1\quad 2\quad 1\\{\color {red}1}\quad 3\quad 3\quad 1\\1\quad {\color {red}4}\quad 6\quad 4\quad 1\\1\quad 5\quad {\color {red}10}\quad 10\quad 5\quad 1\\1\quad 6\quad 15\quad {\color {red}20}\quad 15\quad 6\quad 1\\1\quad 7\quad 21\quad 35\quad {\color {red}35}\quad 21\quad 7\quad 1\\\end{array}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/af25d14ddc89c310f7506f9f56ddf5dc09e27e81 height: height attribute not set width: width attribute not set description: {\displaystyle 2^{n},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0e56bcd84cb03d40ed87c48a090b4c1a0f771084 height: height attribute not set width: width attribute not set description: {\displaystyle m_{n}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ef500a9c1a14c9859524ad7ffbc2643bea3e5703 height: height attribute not set width: width attribute not set description: {\displaystyle 3^{2}=2^{3}+1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3520923fef525ad76dd51b4be9c0c3b9dec4a524 height: height attribute not set width: width attribute not set description: {\displaystyle (n>2)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5ecb33874e99bab1fa69f211dc20d588de7b2602 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {t_{n^{2}}}{n}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4d9241493be76739f2400f258f32c24f9689161f height: height attribute not set width: width attribute not set description: {\displaystyle t_{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/472f05f9dc7a271e59910378a1c418fd6f854fc9 height: height attribute not set width: width attribute not set description: {\displaystyle 1,3,15,4095} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b3627c0691b88fb154d601a38df614e59cd21b6e height: height attribute not set width: width attribute not set description: {\displaystyle 2^{n}-7=x^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a75a3475b3bd6c6561c4d80a128bcf71cb2c1e78 height: height attribute not set width: width attribute not set description: {\displaystyle n=3,4,5,7,15} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/257030caae597fd034c2cbcff2cff9dfc4272d20 height: height attribute not set width: width attribute not set description: {\displaystyle n>3} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/133081604e49aeb1fe815b01af89113b8a3d6dea height: height attribute not set width: width attribute not set description: {\displaystyle m_{n-3}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/6/6c/pascalfibonacci.svg/220px-pascalfibonacci.svg.png height: 253 width: 220 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/08bf3edb177c042d1d7138b914b2826b872bc242 height: height attribute not set width: width attribute not set description: {\displaystyle f_{0}=3} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/494785dc8626d8494a06a12fd5f0e0e952f9fb25 height: height attribute not set width: width attribute not set description: {\displaystyle cat_{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e303a9fc2b2d32f4a8e53599babb6e2ada6ef0e9 height: height attribute not set width: width attribute not set description: {\displaystyle cat_{n}=s_{n+1}^{[n]}-s_{n+2}^{[n-1]}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/339e20666ce9a7531f9b8a6deed88b149a1e87ff height: height attribute not set width: width attribute not set description: {\displaystyle s(n,m)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/37261a042d58d1564d3d06217414607803244508 height: height attribute not set width: width attribute not set description: {\displaystyle t_{n}=s(n+1,n)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1ba039508ab723a5cc9a7688a45f2d002cd9128f height: height attribute not set width: width attribute not set description: {\displaystyle s(n,2)+1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8afaed0172274299d068445d247c03a3c1c16c9a height: height attribute not set width: width attribute not set description: {\displaystyle q_{2}^{[n]}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/52d9f9637833e09aa2d6a5d27d278891ea9a0ee9 height: height attribute not set width: width attribute not set description: {\displaystyle q_{n}^{[d]}=\sum _{m=0}^{d}{s(d,m)n(n-1)\dots (n-m+1)}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bb99ba3704b1bc10739f63321d7b6024377b21c3 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {a}{n_{1}}}+{\frac {b}{n_{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2b76fce82a62ed5461908f0dc8f037de4e3686b0 height: height attribute not set width: width attribute not set description: {\displaystyle k} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ee784b70e772f55ede5e6e0bdc929994bff63413 height: height attribute not set width: width attribute not set description: {\displaystyle n_{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/840e456e3058bc0be28e5cf653b170cdbfcc3be4 height: height attribute not set width: width attribute not set description: {\displaystyle n_{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b2fd8c9944368680c0ea5bc60ddb1e73acea4ef2 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {bn_{1}}{n_{2}}}=kn_{1}-a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1fe438d8f302747aeaf401ebd1726b51731eba11 height: height attribute not set width: width attribute not set description: {\displaystyle bn_{1}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/c/c9/wikipedia_interwiki_section_gear_icon.svg/14px-wikipedia_interwiki_section_gear_icon.svg.png height: 14 width: 14 description: Перейти к шаблону «Последовательности и ряды» |
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https://upload.wikimedia.org/wikipedia/commons/thumb/8/8a/oojs_ui_icon_edit-ltr-progressive.svg/14px-oojs_ui_icon_edit-ltr-progressive.svg.png height: 14 width: 14 description: Перейти к элементу Викиданных |
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https://upload.wikimedia.org/wikipedia/commons/thumb/e/e0/green_star_boxed.svg/24px-green_star_boxed.svg.png height: 24 width: 24 description: ✯ |
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https://login.wikimedia.org/wiki/special:centralautologin/start?type=1x1 height: 1 width: 1 description: no alt description found |
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http://ru.wikipedia.org/static/images/footer/wikimedia-button.svg height: 29 width: 84 description: wikimedia foundation |
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http://ru.wikipedia.org/w/resources/assets/poweredby_mediawiki.svg height: 31 width: 88 description: powered by mediawiki |
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