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Math Help - Convergence with multiple variables

  1. #1
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    Convergence with multiple variables

    Find the positive values of p for which the series converges:

    \sum_{n=2}^{\infty} \frac {1}{n (\ln  n)^p}
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  2. #2
    Moo
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    Hello,

    Take a look at this : Bertrand Series
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    OK go through with the integral test

    \int_1^{\infty}\frac{1}{n\ln(n)^{p}}dn= \frac{(\ln(n))^{-p+1}}{-p+1}+C and I think you can see where to go from there...just remmber that it must converge(the integral) for the series to converge..oh yeah and if p=1 then the antiderivative is \ln(\ln(n)) +C
    Last edited by Mathstud28; April 6th 2008 at 11:13 AM.
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  4. #4
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    But you did it from 1 to infinity, and it is 2 to infinity.......
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  5. #5
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    Do it when n=2 and apply the integral test.
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  6. #6
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    Lemme check my answer, is it when p > 1?
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  7. #7
    MHF Contributor Mathstud28's Avatar
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    Yes

    I think thats right
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