Let and . Suppose that we compound at a rate of at a frequency of times per year.

Then the return over the course of a year is: . If we compound continuously, we obtain a return of .

I want to show that continuous compounding yields a higher return than any other frequency of compounding, or that for all . I approached this by trying to prove that for and then showing that is the supremum of the series

I am having trouble showing that - any hints? Thanks!