Deriving the PGF for Binomial Distribution using 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.

 

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