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 + u² + . . . = 1 / (1-u) if |u| < 1

here u = [exp(t) / 2 ]


try the following page for mgf of binomial distribution