Given the table, write an expression for the function, and describe what it does. a) y = 2x. y is double x. b) y = 3x. y is triple x. c) y = 2x + 1. y is twice x plus 1. d) y = 2x - 1. y is twice x minus 1.

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.