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Math Help - Convergence of Series

  1. #1
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    Convergence of Series

    Please help me with this!!!

    Determine if the following series converge or diverge.

    a) the sum from n=1 to infinity of [n/3n+1]^2n


    b) the sum from n=2 to infinity of [1/(n(ln)^1/2)]


    I don't know what test to use with this series (comparison, ratio, integral etc)?

    thank you for your help
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  2. #2
    Super Member flyingsquirrel's Avatar
    Joined
    Apr 2008
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    Hi

    Quote Originally Posted by kithy View Post
    Please help me with this!!!

    Determine if the following series converge or diverge.

    a) the sum from n=1 to infinity of [n/3n+1]^2n
    I don't know what test to use with this series (comparison, ratio, integral etc)?
    The comparison test works : 0\leq \frac{n}{3n+1}=\frac{1}{3+\frac{1}{n}}\leq \frac{1}{3}

    b) the sum from n=2 to infinity of [1/(n(ln)^1/2)]

    I don't know what test to use with this series (comparison, ratio, integral etc)?
    You can use integrals : \int \frac{1}{t \sqrt{\ln t}} \,\mathrm{d}t=2\int \frac{u'(t)}{2\sqrt{u(t)}} \, \mathrm{d}t with u(t)=\ln t can be quite easily evaluated.
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