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Math Help - series

  1. #1
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    series

    Test the convergence of \sum_{n=0}^\infty \frac{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{k-1}}{\ln (k)}.

    I try to use ratio test but I am stuck in summing up the numerator part.

    Can anyone help me?
    Last edited by CaptainBlack; February 16th 2011 at 06:18 AM. Reason: make the LaTeX readable
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  2. #2
    MHF Contributor chisigma's Avatar
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    The first step in order to extablish if a series \displaystyle \sum_{n=0}^{\infty} a_{n} converges or not is to verify the \displaystyle \lim_{n \rightarrow \infty} a_{n}. How can we say in this case?...

    Kind regards

    \chi \sigma
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by problem View Post
    Test the convergence of \sum_{n=0}^\infty \frac{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{k-1}}{\ln (k)}.

    I try to use ratio test but I am stuck in summing up the numerator part.

    Can anyone help me?
    You might consider making the summand depend on the summation variable:

    \displaystyle \sum_{k=0}^\infty \frac{1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{k-1}}{\ln (k)}.

    Now re-read chisigma's post.
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