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Math Help - Is series Convergent or Divergent? Find sum if convergent.

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    Is series Convergent or Divergent? Find sum if convergent.

    Is series Convergent or Divergent? Find sum if convergent.

    \sum\limits_{i=1}^{infty} \frac{n^3}{n(2n+3)^2}
    Last edited by superduper1; November 18th 2012 at 04:05 PM.
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    Re: Is series Convergent or Divergent? Find sum if convergent.

    \sum\limits_{n=1}^{\infty} \frac{n^3}{n(2n+3)^2}

    \sum\limits_{n=1}^{\infty} \frac{n^3}{4n^3 + 12n^2+ 9n}

    \sum\limits_{n=1}^{\infty} \frac{1}{4 + \frac{12}{n}+ \frac{9}{n^2}}

    \lim_{n\to\infty}\frac{1}{4 + \frac{12}{n}+ \frac{9}{n^2}}  = \frac{1}{4} \neq 0

    so answer is "divergent"?
    Last edited by superduper1; November 18th 2012 at 05:39 PM.
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  3. #3
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    Re: Is series Convergent or Divergent? Find sum if convergent.

    yes
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