A company manufactures thingamajigs. The total weekly cost (in dollars) of producing x thingamajigs is given by

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.