The charity gala will cost $546 if it has 42 attendees. How many attendees can there be, at most, if the budget for the charity gala is $559? Assume the
relationship is directly proportional.

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.