# Summation with combinations

Darth Frodo

## Homework Statement

I'm trying to derive the PGF for the Binomial.

## The Attempt at a Solution

I have it whittled down to $\sum^{n}_{x=0}(nCx)(\frac{sp}{1-p})^x$

I just don't know how to simplify this further. Any help is most appreciated.

$$(x + y )^n = \sum_{k = 0}^n \binom{n}{k} x^{n-k} y^k.$$