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Math Help - I officially loathe infinite series...

  1. #1
    Senior Member mollymcf2009's Avatar
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    I officially loathe infinite series...

    Conditionally convergent, absolutely convergent or divergent?

    \sum^{\infty}_{n=1} \frac{12^n}{(n+1)8^{2n+1}}
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Positive series implies that the convergence is absolute, thus, prove that the series converges and you'll get absolute convergence.
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  3. #3
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by Krizalid View Post
    Positive series implies that the convergence is absolute, thus, prove that the series converges and you'll get absolute convergence.
    So would I use

    \frac{1}{n+1}

    to do this?
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by mollymcf2009 View Post
    So would I use

    \frac{1}{n+1}

    to do this?
    No, because it looks similar to the harmonic series term \frac{1}n which would then suggest that the series diverges.

    I would suggest comparing this to \frac{12^n}{8^{2n}}=\left(\frac{3}{16}\right)^n which is geometric.
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