How to approach simplifying the following sum: $$ \sum_{x=0}^kx\binom{k}{x}\left(\frac{k-x}{k}\right)^d $$ any advice is welcome!
UDP. equation updated, there was a typo.
2026-04-01 14:19:08.1775053148
Simplify sum with binomial coefficients?
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Ok, after a while, it can be shown that: $\sum_{x=0}^kx\binom{k}{x}\left(\frac{k-x}{k}\right)^d = k\left(1-\frac{1}{k}\right)^d$.