I'm trying to prove that 3^n is a member of O(2^2n) by demonstrating that

the limit as n approches infinity of 3^n/2^2n is 0. However, if my calculus (or really algebra is correct, this ratio simplifies to 3^n/4^n which further simplifies to (3/4)^n, the limit of which would be infinity as n approaches infinity. Am I missing something?