a.$k,n\epsilon \mathbb{N},k\leqslant n.$.
$(-1)^{k}C_{k}^{k}C_{n}^{k}+(-1)^{k+1}C_{k+1}^{k}C_{n}^{k+1}+....+(-1)^{n}C_{n}^{k}C_{n}^{n}=0$.
b.$1(C_{n}^{1})^{2}+2(C_{n}^{2})^{2}+...+n(C_{n}^{n})^{2}=\frac{(2n)!}{(n-1)!(n-1)!}$.
a.$k,n\epsilon \mathbb{N},k\leqslant n.$.
$(-1)^{k}C_{k}^{k}C_{n}^{k}+(-1)^{k+1}C_{k+1}^{k}C_{n}^{k+1}+....+(-1)^{n}C_{n}^{k}C_{n}^{n}=0$.
b.$1(C_{n}^{1})^{2}+2(C_{n}^{2})^{2}+...+n(C_{n}^{n})^{2}=\frac{(2n)!}{(n-1)!(n-1)!}$.
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