Chu-Vandermonde Identity/Proof 1

Theorem
Let $r, s \in \R, n \in \Z$.

Then:


 * $\displaystyle \sum_k \binom r k \binom s {n-k} = \binom {r+s} n$

where $\displaystyle \binom r k$ is a binomial coefficient.

Proof 1
As this has to be true for all $x$, we have that:
 * $\displaystyle \binom {r+s} n = \sum_k \binom r k \binom s {n-k}$