Is series Convergent or Divergent? Find sum if convergent.

**superduper1** · November 18th 2012, 05:37 AM

Is series Convergent or Divergent? Find sum if convergent.

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

**superduper1** · November 18th 2012, 04:16 PM

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

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

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

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

so answer is "divergent"?

**skeeter** · November 18th 2012, 05:14 PM

yes

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Is series Convergent or Divergent? Find sum if convergent.

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