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Math Help - determine converges absolutely, conditonally or if diverges

  1. #1
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    determine converges absolutely, conditonally or if diverges

    heres the equation: http://img440.imageshack.us/img440/6467/untitledbw7.jpg

    I showed that it was an alternate series, and i predicted that it converges absolutely, however i'm missing steps.

    help is needed.
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  2. #2
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    Hello, rcmango!

    Heres the series: . \sum^{\infty}_{n=0}\frac{(-1)^nn}{\sqrt{1 + n^6}}

    I showed that it was an alternating series,
    and i predicted that it converges absolutely.
    However, i'm missing steps.

    Comparison test

    \frac{n}{\sqrt{1 + n^6}} \:< \:\frac{n}{\sqrt{n^6}} \:=\:\frac{n}{n^3}\:=\:\frac{1}{n^2}

    Hence: . \sum^{\infty}_{n=1}\frac{n}{\sqrt{1+n^6}} \:< \:\sum^{\infty}_{n=1}\frac{1}{n^2} . . . a convergent p-series

    Therefore: . \sum^{\infty}_{n=0}\frac{n}{\sqrt{1+n^6}} converges.

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  3. #3
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    this is converging to 0 correct?

    also, by showing the steps you've provided, would this be enough satisfactory work for proof of this answer.

    thanks.
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