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Math Help - Series question

  1. #1
    Member akhayoon's Avatar
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    Series question

    \sum(-1)^{n}\frac{1+n}{n^{2}-n}

    in the sum n=2 and goes to infinity

    so is the sequence divergent, conditionally convergent or absolutely convergent?

    so I chose conditionally convergent because of the (-1)^n

    but the limit comparison test tells me that the series is divergent since 1/n is divergent....so does this problem work out?
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi

    The limit comparison test only apply for series with positive terms, the only things you might get is that \sum \frac{1+n}{n^2-n} is divergent.

    so I chose conditionally convergent because of the (-1)^n
    It's not because there is (-1)^n that the series satisfy the alternating test. (you also need to show that \frac{1+n}{n^2-n} decreases and that \lim_{n\to \infty}\frac{1+n}{n^2-n}=0)
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by akhayoon View Post
    \sum(-1)^{n}\frac{1+n}{n^{2}-n}

    in the sum n=2 and goes to infinity

    so is the sequence divergent, conditionally convergent or absolutely convergent?

    so I chose conditionally convergent because of the (-1)^n

    but the limit comparison test tells me that the series is divergent since 1/n is divergent....so does this problem work out?
    Two words...Ratio test
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