# Limits of Exponentials

• June 12th 2011, 01:46 PM
kaiser0792
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?
• June 12th 2011, 02:42 PM
pickslides
Quote:

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 $\displaystyle \lim_{n\to \infty}\left( \frac{3}{4}\right)^n = 0$
• June 12th 2011, 04:10 PM
kaiser0792
Of course, you are correct. Blind spot, I guess! Thanks!!