# Math Help - Limits of Exponentials

1. ## Limits of Exponentials

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?

2. Originally Posted by kaiser0792
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.
I see it as $\displaystyle \lim_{n\to \infty}\left( \frac{3}{4}\right)^n = 0$

3. Of course, you are correct. Blind spot, I guess! Thanks!!