Now use the moment generating function from Exercise 43.1 to verify that, if X is Geometric with

Question:

Now use the moment generating function from Exercise 43.1 to verify that, if X is Geometric with parameter p, then E(X2) = (2 - p)/p2.
In Exercise 1
P(X = x) = px(x) = (1- p)x-lp
For x = 1, 2, 3,...,
and pX(x) = 0 otherwise), then find the moment generating function of X.