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Math Help - cauchy condensation test

  1. #1
    Junior Member
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    cauchy condensation test

    Hello to all,
    the cauchy condensation test says:
    sum(a_n) converges if and only if sum (2^n)(a_(2^n)) converges.
    So how do we pronve using this test the divergence of
    1) sum 1/(n.lnn)
    and
    2) sum 1/((n)(lnn)(lnlnn))
    please urgent
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  2. #2
    MHF Contributor chisigma's Avatar
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    From \sum_{n=2}^{\infty} \frac{1}{n\cdot \ln n} the Cauchy condensation test considers \sum_{n=2}^{\infty} \frac {2^{n}}{2^{n} \cdot \ln (2^{n})} = \sum_{n=2}^{\infty} \frac{1}{n\cdot \ln 2} that diverges...

    From \sum_{n=2}^{\infty} \frac{1}{n\cdot \ln n \cdot \ln (\ln n)} the Cauchy condensation test considers \sum_{n=2}^{\infty} \frac {2^{n}}{2^{n} \cdot \ln (2^{n}) \cdot \ln (\ln (2^{n})} = \sum_{n=2}^{\infty} \frac{1}{n\cdot \ln 2\cdot \ln (n \cdot \ln 2)} that diverges...

    Kind regards

    \chi \sigma
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