Characteristic equation of binomial random variable

[sinned4789]

Homework Statement

find the characteristic equation of a binomial variable with pmf p(x) =\frac{n!}{(n-k)!k!}*p^{k}*(1-p)^{n-k}

Homework Equations

characteristic equation
I(t) = \sump(x)*e^{tk}

The Attempt at a Solution

I(t) = \sum\frac{n!}{(n-k)!k!}*(p^{k}*(1-p)^{-k}*e^{tk})*(1-p)^{n}

i am stuck on this series because i don't know what to do with the combination term.

 

[LCKurtz]

In the definition

E(tX) = \sum_{k-0}^{n}\binom n k e^{tk}p^k(1-p)^{n-k}

group the e^tk with the p^k and then think about what the binomial expansion of (a + b)ⁿ looks like.