Hi, I am studying discrete random variables and have been given the question:

Suppose that X is a geometrically distributed random variable with parameter p €(0,1) i.e for all n=1,2..... P(X=n)=(1-p)^(n-1)p

Show that for k=0,1,......

P(X>k)=(1-p)^k

In the previous part of the question I proved that E(X)=1/p, will the formula

E(X)=sum(P(X>n)) where n € 0,1,2..... help me?

Thanks for your help