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Math Help - Absolute convergence & root/ratio tests

  1. #1
    Senior Member mollymcf2009's Avatar
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    Absolute convergence & root/ratio tests

    Absolutely convergent, conditionally convergent or divergent?

    \sum^{\infty}_{n=1}  \frac{(-1)^{n+1}}{\sqrt[3]{n}}

    I thought that this would be divergent via the p-series test with p<1 but that isn't correct. What do I do with this?
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    |a_n|=\frac1{\sqrt[3]n} so it does not coverge absolutely.

    Now, use Leibniz test if the original converges, if so, thus the series converges conditionally.
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