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Math Help - Does it convert or not?

  1. #1
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    Does it convert or not?

    This is a row and im supposed to determine if it does convert, or goes against infinity (divergens is the norwegian word for this)

    Sum between n=1 and infinity: ((-1)^n*n+1)/n^2

    I really need to do this one before my test
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    The given series is the sum of series:

    (i)\; \displaystyle\sum_{n=1}^{+\infty}\dfrac{(-1)^n}{n}\quad (ii)\;\displaystyle\sum_{n=1}^{+\infty}\dfrac{1}{n  ^2}

    The former is an alternating series, use the Leibnitz test to prove that is convergentt. The latter is convergent ( p series with p>1 ). The sum of two convergent series is convergent.
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