# Is series Convergent or Divergent? Find sum if convergent.

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• November 18th 2012, 06:37 AM
superduper1
Is series Convergent or Divergent? Find sum if convergent.
Is series Convergent or Divergent? Find sum if convergent.

$\sum\limits_{i=1}^{infty} \frac{n^3}{n(2n+3)^2}$
• November 18th 2012, 05:16 PM
superduper1
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"?
• November 18th 2012, 06:14 PM
skeeter
Re: Is series Convergent or Divergent? Find sum if convergent.
yes