Find the common ratlo for the following sequence. 1/2, -1/4, 1/8, -1/16, ...

1/2

-2

-1/2

2

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.