A movie theater charges $75 to rent out the theater and they charge
$12 per popcorn/drink combo. If Ms.
Mullen goes to the movie theater:
invites 12 other family members, and
everyone gets a combo, how much will it
cost in total?

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.