# Summation Proof with Binomial Theorem

1. May 21, 2007

### ChaoticLlama

Prove the following statement:

$$$\sum\limits_{r + s = t} {\left( { - 1} \right)^r \left( \begin{array}{c} n + r - 1 \\ r \\ \end{array} \right)} \left( \begin{array}{c} m \\ s \\ \end{array} \right) = \left( \begin{array}{c} m - n \\ t \\ \end{array} \right)$$$

Any initial help is appreciated.

2. May 26, 2007

### cristo

Staff Emeritus
Well, what have you done? What is the definition of, say, m choose s?