**The discrete random variable X has probability function**

p(x)=4/(5^X+1) X=0, 1, 2,...

Derive the MGF of X and use it to find E(X) and V(X).

p(x)=4/(5^X+1) X=0, 1, 2,...

Derive the MGF of X and use it to find E(X) and V(X).

I have managed to get this far:

Mx(t) = Σ(e^tX)(4/(5^X+1))

e^(tX) = 1 + tX + (t^2/2!)X^2 + (t^3/3!)X^3 + ...

So Mx(t) = Σ(4/(5^X+1)) + tΣ(4/(5^X+1)) + (t^2/2!)Σ(4/(5^X+1)) + (t^3/3!)Σ(4/(5^X+1)) + ...

But I have no idea where to go from here, any help would be much appreciated!