Prove $\sum_{i=0}^n \binom{x + n - i}{n - i} \binom{y + i}{i} = \binom{x+y+n+1}{n}$.

Asked Mar 17 '21 at 14:58

Active Mar 17 '21 at 14:58

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Prove $\sum_{i=0}^n \binom{x + n - i}{n - i} \binom{y + i}{i} = \binom{x+y+n+1}{n}$. I put it into Mathematica and it gives answer. However, I have no idea how to prove it. Could anyone help me? Thanks!

asked Mar 17 '21 at 14:58

Coned Zot

Prove $\sum_{i=0}^n \binom{x + n - i}{n - i} \binom{y + i}{i} = \binom{x+y+n+1}{n}$.

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