Chu-Vandermonde Identity

Theorem
Let $r, s \in \R, n \in \Z_{\ge 0}$.

Then:
 * $\ds \sum_{k \mathop = 0}^n \binom r k \binom s {n - k} = \binom {r + s} n$

where $\dbinom r k$ is a binomial coefficient.

Also known as
When $r$ and $s$ are integers, it is more commonly known as Vandermonde's identity or Vandermonde's convolution (formula).

Sometimes it is seen referred to as the Chu-Vandermonde formula, or Vandermonde's theorem.