Hi. I have a problem with this question:

Let $\displaystyle X$ be a discrete uniform random variable with pmf $\displaystyle p_{X}(x)=\frac{1}{N}$, for $\displaystyle x=1,2,...,N$. Find the mgf of $\displaystyle X$.

What I did was:

$\displaystyle M_{X}(t)=E[e^{tx}]$

$\displaystyle =\sum_{x=1}^N e^{tx}\frac{1}{N}$

$\displaystyle =\frac{1}{N} \sum_{x=1}^N e^{tx}$

I don't know how to continue after that