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Math Help - Converge/Diverge help

  1. #1
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    Converge/Diverge help

    I have to determine whether these series converge or diverge and i got stuck on 2 of them

    the first one is 1/ (n) (squareroot n)

    and the second one is n-1/(n^2) (squareroot n)

    any idelas how to do either of these two?
    Thanks
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    \sum\limits_{n=1}^{\infty }{\frac{1}{n\sqrt{n}}}=\sum\limits_{n=1}^{\infty }{\frac{1}{{{n}^{3/2}}}}<\infty , 'cause it's a convergent p-series with p=\frac32>1.

    For your second question, \sum\limits_{n=2}^{\infty }{\frac{n-1}{{{n}^{2}}\sqrt{n}}}\le \sum\limits_{n=2}^{\infty }{\frac{n}{{{n}^{2}}\sqrt{n}}}=\sum\limits_{n=2}^{  \infty }{\frac{1}{n\sqrt{n}}}<\infty, convergent by the above reason.
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