Trinity bought two 6-foot long boards to make a set of shelves. if she cuts each shelf to a length of 24 inches, how many shelves can she make from those boards?

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.