File:Pascal triangle extended.svg
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Summary
| Description |
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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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:04, 29 March 2021 | | 512 × 341 (54 KB) | Cmglee | Remove duplicated elements. |
| 17:59, 28 March 2021 |  | 512 × 341 (295 KB) | Cmglee | Add fractional ''n''. | |
| 03:25, 20 March 2021 |  | 512 × 640 (31 KB) | Cmglee | {{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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