Dan borrowed $750.00 from his brother who is charging him 8% simple interest. if dan pays his brother back in 6 months, how much does he have to pay back including the interest?

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.