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Thread: Another limit question...

  1. #1
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    Another limit question...

    $\displaystyle \lim_{n\rightarrow\infty}\frac{2^n+(-2)^n}{3^n}$

    Here is my work:
    $\displaystyle \lim\frac{2^n(1+(-1))}{2^{n*ln(3)}} $
    since ln(3)>1 it goes to positive infinity but thatprobably wasn´t a brilliant thought...any ideas what went wrong here?
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  2. #2
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    Quote Originally Posted by Henryt999 View Post
    $\displaystyle \lim_{n\rightarrow\infty}\frac{2^n+(-2)^n}{3^n}$

    Here is my work:
    $\displaystyle \lim\frac{2^n(1+(-1))}{2^{n*ln(3)}} $
    since ln(3)>1 it goes to positive infinity but thatprobably wasn´t a brilliant thought...any ideas what went wrong here?

    $\displaystyle \color{blue}\lim_{n\rightarrow\infty}\frac{2^n+(-2)^n}{3^n}=\lim_{n\to\infty} (\frac{2}{3})^n+\lim_{n\to\infty}(\frac{-2}{3})^n$
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  3. #3
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    $\displaystyle \frac{2^n+(-2)^n}{3^n}=\left(\frac{2}{3}\right)^n+\left(\frac{-2}{3}\right)^n$
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