Handsome happyguy with another equation for you to help him

Revision en2, by yspm, 2021-10-29 11:20:54

happyguy656 just became a Grandmaster and he wants you to help him to prove the below equation:

$$$\sum_{i=1}^{n} i\binom {n-1}{n-i}\begin{Bmatrix} {n-i}\\{k-1}\end{Bmatrix}=\begin{Bmatrix}n \\ k\end{Bmatrix}+(n-1)\begin{Bmatrix}{n-1}\\ k\end{Bmatrix}$$$

Let $$$\binom nm$$$ be $$$0$$$ when $$$n<m$$$ and n,k are given integers


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en2 English yspm 2021-10-29 11:20:54 41
en1 English yspm 2021-10-29 11:19:52 437 Initial revision (published)