Well just write the expectation :
but the sum is the power series of , hence the result.
Why is it restricted to |t|<1/p ? Because otherwise, the series doesn't converge.
A discrete random variable X has a probability mass function given by
px (x) = (k(p^x))/x for x=1,2...
where p is a constant such that 0 < p < 1 and k = -1/ln(q) where q = 1-p
a) Show that the probability generating function of X is given by
E(t^x) = (ln(1 - pt))/ln(q) for |t| < 1/p
b) Why must t be restricted to this range?
any help is greatly appreciated!