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Math Help - Comparison test question

  1. #1
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    Comparison test question

    hi everyone

    need help with this question:

    Use comparison test to determine the convergent of the following series:

    1,\frac{1}{2^2},\frac{1}{3^3},\frac{1}{4^4}

    i found the general form, \frac{1}{n^n} but i cant do the comparison. needhelp & guidance for this question.

    really appreciate all your help & support.
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  2. #2
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    I think it converges but I'm not sure what's the best comparison, it's already too simple. My inspection is based on a case like s_n = \frac{1}{n2^n} for instance, when you can just compare it with \sum \frac{1}{2^n} and you know it converges.
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  3. #3
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    thank you for replying. just wondering how to prove it converges...stuck.

    need some help on this problem.

    thank you for all help & support,appreciated.
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  4. #4
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    n^n\geq n^2 \forall n>2 \implies \frac{1}{n^2}\geq \frac{1}{n^n} \forall n>2
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