After eating dinner at a restaurant, your bill before tax and tip was $72.50. The sales tax rate is 8% and you decide to leave a 20% tip based on the bill after tax was added. What is the total cost of the dinner?

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.