Chu-Vandermonde Identity/Examples/2 from e + pi/Proof 1

Example of Use of Chu-Vandermonde Identity

Let $r = e$, $s = \pi$ and $n = 2$

$\ds \binom {e + \pi} 2 = \sum_{k \mathop = 0}^2 \binom e k \binom \pi {2 - k}$

Proof

From the Chu-Vandermonde Identity:

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

The result follows on setting $r = e$, $s = \pi$ and $n = 2$.

$\blacksquare$