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Math Help - Limits of Exponentials

  1. #1
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    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?
    Last edited by mr fantastic; June 12th 2011 at 02:17 PM. Reason: Made readable.
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  2. #2
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    Quote Originally Posted by kaiser0792 View Post
    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
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  3. #3
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    Of course, you are correct. Blind spot, I guess! Thanks!!
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