We went over this material once in class and we have a bunch of problems that we have to do, and I still don't know if I understand the concept fully. One of the problems is:

Find the moment-generating function of the discrete random variable X that has the probability distribution

f(x) = 2(1/3)^x for x = 1, 2, 3, ...

and use it to determine the values of mu1' and mu2'.

So I tried to use the definition, which says that Mx(t) = E(e^(tx)) = Integral from -INF to INF of (e^(tx))*f(x)dx.

I got the Integral from 1 to INF of (e^(tx))*(2(1/3)^x)dx, but now I am lost... any help would be GREATLY appreciated.