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Math Help - How to show this converges to 0

  1. #1
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    How to show this converges to 0

    Prove that
    \frac{2^x}{3^{2x+1}} converges to 0 as x approaches infinity.

    Not quite sure how to begin this. I know that it's true, but I don't know how to prove it using definitions and theorems. Any hints?
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  2. #2
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    Quote Originally Posted by paupsers View Post
    Prove that
    \frac{2^x}{3^{2x+1}} converges to 0 as x approaches infinity.
    \left| r \right| < 1\, \Rightarrow \,\lim _{n \to \infty } r^n  = 0.

    \frac{{2^x }}<br />
{{3^{2x + 1} }} = \frac{1}<br />
{3}\left( {\frac{2}<br />
{9}} \right)^x
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  3. #3
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    Quote Originally Posted by paupsers View Post
    Prove that
    \frac{2^x}{3^{2x+1}} converges to 0 as x approaches infinity.

    Not quite sure how to begin this. I know that it's true, but I don't know how to prove it using definitions and theorems. Any hints?

    \frac{2^x}{3^{2x+1}}=\frac{1}{3}\left(\frac{2}{9}\  right)^x , and I hope you know that if |x|<1\,\,then\,\,x^n\xrightarrow [n\to\infty] {} 0...

    Tonio
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