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Thread: determine convergence or divergence of series

  1. #1
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    determine convergence or divergence of series

    summation from n=1 to infinity ((n+1)0.5-(n)0.5)/(n2+n)​0.5.

    I've tried using limit comparison test but the ratio i got approaches 0 and thus no conclusion can be drawn.
    Last edited by noobpronoobpro; May 16th 2017 at 06:59 AM.
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  2. #2
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    Re: determine convergence or divergence of series

    note ...

    $\dfrac{\sqrt{n+1} - \sqrt{n}}{\sqrt{n^2+n}} \cdot \dfrac{\sqrt{n+1} + \sqrt{n}}{\sqrt{n+1} + \sqrt{n}} = \dfrac{1}{\sqrt{n^2+n} (\sqrt{n+1} + \sqrt{n})} < \dfrac{1}{\sqrt{n^3}}$

    what can you say about the series, $\displaystyle \sum \dfrac{1}{n^{3/2}}$ ... ?
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  3. #3
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    Re: determine convergence or divergence of series

    thats a p-series with power greater than 1 and hence converge. using comparison test, the series given also converge, Thanks for the help
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