A gym charges each member $100 for the first month, which includes a membership fee, and $50 per month for each month after that. How much money
will a person spend on their gym membership for 6 months?

Let x have probability generating function gx (s) and let un generating function u(s) of the sequence uo, u1, satisfies p(x > n). show that the (1- s)u(s) = 1 - gx(s), whenever the series defining these generating functions converge.