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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 .
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Author Cmglee

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Date/TimeThumbnailDimensionsUserComment
current19:04, 29 March 2021Thumbnail for version as of 19:04, 29 March 2021512 × 341 (54 KB)CmgleeRemove duplicated elements.
17:59, 28 March 2021Thumbnail for version as of 17:59, 28 March 2021512 × 341 (295 KB)CmgleeAdd fractional ''n''.
03:25, 20 March 2021Thumbnail for version as of 03:25, 20 March 2021512 × 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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