# Inductive Proof for Vandermonde's Identity?

I am reading up on Vandermonde's Identity, and so far I have found proofs for the identity using combinatorics, sets, and other methods. However, I am trying to find a proof that utilizes mathematical induction. Does anyone know of such a proof?

For those who don't know Vandermonde's Identity, here it is:

For every $m \ge 0$, and every $0 \le r \le m$, if $r \le n$, then

$$\binom{m+n}r = \sum_{k=0}^r \binom mk \binom n{r-k}$$

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