Proving convergence of divergence of a series.

**Benno_11** · May 24th 2009, 12:58 AM

Thanks for the help... there is one more that I can't get.

$\sum_{n=1}^{\infty} \frac{n}{n \sqrt{n} + 2}$

I just have trouble seeing how to prove they converge or diverge. I guess I just need to practicing them!

**mr fantastic** · May 24th 2009, 01:14 AM

Originally Posted by Benno_11

Thanks for the help... there is one more that I can't get.

$\sum_{n=1}^{\infty} \frac{n}{n \sqrt{n} + 2}$

I just have trouble seeing how to prove they converge or diverge. I guess I just need to practicing them!

Note that $\frac{n}{n \sqrt{n} + 2} > \frac{n}{n \sqrt{n} + n \sqrt{n}}$ for $n > 1$ . Now use the comparison test.

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