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Math Help - Series questions!

  1. #1
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    Series questions!

    (3) / n sqrt(n)

    not sure what test i should use for this problem!


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    [( -1 )^n] * [3^(n-2)] / 2^n

    i dont understand why i cannot use this root test for this problem...it seems to work out fine and i get the limit = 0 so since L < 1 then it should be convergent....but this is actually supposed to be divergent.



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    10n+3 / n2^n

    another one i'm not sure which test i should use
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by lochnessmonster View Post
    (3) / n sqrt(n)

    not sure what test i should use for this problem!


    -----------------------------------------------------

    [( -1 )^n] * [3^(n-2)] / 2^n

    i dont understand why i cannot use this root test for this problem...it seems to work out fine and i get the limit = 0 so since L < 1 then it should be convergent....but this is actually supposed to be divergent.



    ----------------------------------------------------------

    10n+3 / n2^n

    another one i'm not sure which test i should use
    I am having a hard time reading the first one my guess is that it is this

    \displaystyle \sum_{n=0}^{\infty}\frac{3}{n\sqrt{n}}=\sum_{n=0}^  {\infty}\frac{3}{n^{\frac{3}{2}}}

    This is a p-series with p=\frac{3}{2}

    \displaystyle \sum_{n=0}^{\infty}\frac{(-1)^n3^{n-2}}{2^n}=3^{-2}\sum_{n=0}^{\infty}\left( \frac{-3}{2} \right)^n

    This is a geometric series or use the basic test for divergence!

    For the last one I think this is the series

    \displaystyle \sum_{n=0}^{\infty}\frac{10n+3}{n2^n}

    Use the limit comparison test with \displaystle b_n=\frac{1}{2^n} this is a convergent geometric series
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by lochnessmonster View Post
    (3) / n sqrt(n)

    Use the integral test.


    [( -1 )^n] * [3^(n-2)] / 2^n

    i dont understand why i cannot use this root test for this problem...it seems to work out fine and i get the limit = 0 so since L < 1 then it should be convergent....but this is actually supposed to be divergent.

    Check your limit (it is not 0) . The limit \lim_{n\to +\infty}( -1 )^n 3^{n-2} / 2^n does not exist, so the series is divergent.


    10n+3 / n2^n another one i'm not sure which test i should use

    Use the ratio test.


    Edited: Sorry, I didn`t see the previous post.
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