CombinatorialIdentity
Intermediate
Show that $$\sum_{k=0}^{2n-1}(-1)^k(k+1)\binom{2n}{k}^{-1}=\frac{1}{\binom{2n}{0}}-\frac{2}{\binom{2n}{1}}+\cdots-\frac{2n}{\binom{2n}{2n-1}}=0$$
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