File:Pascal triangle extended.svg
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Summary[edit]
DescriptionPascal triangle extended.svg |
Binomial coefficients C (n, k) extended for negative and fractional n, illustrated with expansion of a simple binomial by CMG Lee. It can be observed that Pascal's triangle is rotated and alternate terms are negated. The case n = −1 gives Grandi's series. Shaded in blue, n = 0.5 gives : substituting and integrating from 0 to ½ gives half the area of a semicircle minus a circular segment, , yielding Newton's breakthrough method of approximating . |
Source | Own work |
Author | Cmglee |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 19:04, 29 March 2021 | 512 × 341 (54 KB) | Cmglee (talk | contribs) | Remove duplicated elements. | |
17:59, 28 March 2021 | 512 × 341 (295 KB) | Cmglee (talk | contribs) | Add fractional ''n''. | ||
03:25, 20 March 2021 | 512 × 640 (31 KB) | Cmglee (talk | contribs) | {{Information |Description=Binomial coefficients ''C''(''n'', ''k'') extended for negative ''n'' illustrated with expansion of a simple binomial by CMG Lee. It can be observed that Pascal's triangle is rotated and alternate terms are negated. The case ''n'' = −1 gives Grandi's series. |Source={{own}} |Date= |Author= Cmglee |Permission= |other_versions= }} Category:Binomial coefficients Category:Pascal's triangle |
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Short title | Pascal triangle extended |
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Image title | Binomial coefficients C(n, k) extended for negative and fractional n, illustrated with expansion of a simple binomial by CMG Lee. It can be observed that Pascal's triangle is rotated and alternate terms are negated. The case n = −1 gives Grandi's series. |
Width | 100% |
Height | 100% |