Theorema binomiale

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Theorema explicatum per geometriam

Theorema binomiale^[1] seu binominale dicit:

(x + y)^{n} = \sum_{k = 0}^{n} (\binom{n}{k}) x^{n - k} y^{k} (1)

ubi k coefficiens binomialis est.

Latius expressum:

(x + y)^{n} = (\binom{n}{0}) x^{n} + (\binom{n}{1}) x^{n - 1} y + \dots + (\binom{n}{n - 1}) x y^{n - 1} + (\binom{n}{n}) y^{n} = \sum_{k = 0}^{n} (\binom{n}{k}) x^{n - k} y^{k} .

Nota

↑ Prasse, Mauricius: Commentationes Mathematicae, Lipsiae 1804. Cf. p. 4 (Commentationes Mathematicae auctore Mauricio de Prasse. Mathem[aticae] prof[essor] ord[inarius] in univers[itati] liter[arum] Lipsiensi.)

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