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Math Help - direct comparison test

  1. #1
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    direct comparison test

    Hi. I need to show whether this series diverges or converges, by the direct comparison test. But I don't understand what it is that I should compare it to that is helpful.

    \sum_{n=2}^{\infty}\frac{ln\,n}{n+1}
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  2. #2
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    Re: direct comparison test

    Since for n\ge{3}, \ln{n}\ge{1} and 2n>n+1, \frac{\ln{n}}{n+1}>\frac{1}{2n}.

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  3. #3
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    Re: direct comparison test

    Why not just compare it to \sum{\frac{1}{n+1}}?
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