What is the mgf of the geometric random variable with pmf of f(w) = p(1-p)^(w-1), where p = 1/8? Show how to derive it and explain any bounds on the values of t for which it is valid.

So far, I have gotten it simplified to:

M(t) = (1/7) * Sigma( ((7/8)*e^t)^w ) where the sum is from w=0 to infinity.

I don't really know where to go from here to simplify it, or what bounds t could possibly have.