# Summation with combinations

1. Oct 8, 2013

### Darth Frodo

1. The problem statement, all variables and given/known data

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

3. 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.

2. Oct 9, 2013

### CompuChip

I think you lost some $(1 - p)$s there, are you sure you didn't mean $\sum_{x = 0}^n \binom{n}{x} (sp)^x (1 - p)^{n - x}$?

The result should follow from the binomial theorem,
$$(x + y )^n = \sum_{k = 0}^n \binom{n}{k} x^{n-k} y^k.$$