
find MGF given PMF
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

I am assuming you mean discrete geometric distribution with x = 0,1,2, ....
on simplifying mgf = (1/2) ∑ [exp(t) / 2 ]^x where the summation is from 0 to infinity
mgf = (1/2) / { 1 [exp(t) / 2 ] } using the formulae for infinite geometric series (with suitable restriction on t as you said)
note
expand the ∑ and use 1 + u + uČ + . . . = 1 / (1u) if u < 1
here u = [exp(t) / 2 ]
try the following page for mgf of binomial distribution