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Math Help - Convergence, Divergence of a series

  1. #1
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    Convergence, Divergence of a series

    Please check my answers:

    For the following series, determine its convergence or divergence. If it converges, find its sum:

    a) \sum_{n=2}^{\infty} \frac{1}{n^2-1} converges to 0

    b) \sum_{n=1}^{\infty} \frac{n+1}{2n-1} diverges

    c) \sum_{n=2}^{\infty} \frac{n}{ln (n)} diverges



    If some of the above are incorrect, could you please help me fix it?!
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  2. #2
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    Quote Originally Posted by qzno View Post
    Please check my answers:

    For the following series, determine its convergence or divergence. If it converges, find its sum:

    a) \sum_{n=2}^{\infty} \frac{1}{n^2-1} converges to 0

    b) \sum_{n=1}^{\infty} \frac{n+1}{2n-1} diverges

    c) \sum_{n=2}^{\infty} \frac{n}{ln (n)} diverges



    If some of the above are incorrect, could you please help me fix it?!
    (b) and (c) are ok ... the sum of (a) is not 0.

    \sum_{n=2}^{\infty} \frac{1}{n^2-1} = \frac{1}{2} \sum_{n=2}^{\infty} \frac{1}{n-1} - \frac{1}{n+1} = \frac{3}{4}<br />
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