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Math Help - Another limit comparison series

  1. #1
    Senior Member mollymcf2009's Avatar
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    Another limit comparison series

    I suck at these. Anyway, can someone tell me how to start this one please?

    \sum^{\infty}_{n=1} \frac{cos^2(n)}{n^4 + 1}
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  2. #2
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    \frac{\cos ^{2}n}{n^{4}+1}<\frac{1}{n^{4}}.
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  3. #3
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    Recall that: 0 \leq \cos^2 x \leq 1

    So: \frac{\cos^2 n}{n^4 + 1} \leq \frac{1}{n^4 + 1} < \frac{1}{n^4}
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  4. #4
    MHF Contributor matheagle's Avatar
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    Note that 0<cos^2(n)<1. THUS....

    Quote Originally Posted by mollymcf2009 View Post
    I suck at these. Anyway, can someone tell me how to start this one please?

     \sum^{\infty}_{n=1} \frac{cos^2(n)}{n^4 + 1} <\sum^{\infty}_{n=1} \frac{1}{n^4}<\infty
    via p=4
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