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Math Help - series converges.

  1. #1
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    series converges.

    Hi, I know this series converges.

    n^4 * 2^-n

    i used the direct comparison test with 1/2^n

    however, i'm not sure why n^4 would = 1.

    thanks for any help.
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  2. #2
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    Quote Originally Posted by rcmango View Post
    Hi, I know this series converges.

    n^4 * 2^-n

    i used the direct comparison test with 1/2^n

    however, i'm not sure why n^4 would = 1.

    thanks for any help.
    I personally would use the ratio test

     \lim_{n \to \infty}\frac{(n+1)^4}{2^{n+1}} / \frac{n^4}{2^n} = \lim_{n \to \infty}\frac{(n+1)^4}{n^4} \frac{2^{n+1}}{2^2} = 1 \cdot \frac{1}{2} < 1

    so the series converges.
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