A discrete random variable X is pmf p(x)=(1-p)^(x-1)p for x=1,2,...

where 0<p<1

(a) Find the moment generating function of X

(which is pe^t / (1-qe^t)

(b) Hence, or otherwise, find E(X(X-1)...(X-r+1))

So what i am trying to do is:

E(X(X-1)...(X-r+1)

=E(e^(lnx)+e^ln(x-1)+...+e^ln(x-r+1))

=pe^(lnx)/(1-qe^(lnx))*...*pe^ln(x-r+1)/(1-qe^ln(x-r+1)

then I don't know how to proceed, can somebody help ?