The population, P, of Lake Norman with a large number of seasonal residents can be modeled using the function P=3000 sin304 6100, where is the
number of months after New Year's Day. What is the minimum population?

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.