I'm given pmf of X is (1/2)^(x+1) and asked to find the moment generating function.

so i have MGF = sum{(exp(xt))*(1/2)^(x+1)}

sum((1/2)^x) goes to 1.

but the exp(x) either blows up or goes to 0 depending on t...

I think i'm supposed to have a function of t left. Any errors here?

Thanks