#1887 · Algebra · Sequences & series

Finite Series Identity One

If $n$ is a positive integer, shew that $n^{n + 1} - n (n - 1)^{n + 1} + \frac{n ( n - 1 )}{2 !} (n - 2)^{n + 1} - \dots = \frac{1}{2} n (n + 1)!$ , extended to $n$ terms.

~10 minProof · checked by AIFinite differencesBinomial theorem

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXII. Undetermined Coefficients, Examples XXII.b, No. 12 (part 1)

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