#1888 · Algebra · Sequences & series

Finite Series Identity Two

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

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