Originally Posted by

**SworD** Hint: try to put the terms together into one fraction. Then you can apply this general rule:

**If you are dealing with the ratio of two polynomials, the series will converge if and only if the highest power of the denominator exceeds the highest power of the numerator by **__more__ than 1.

For example,

$\displaystyle \sum_{n=1}^{\infty} \frac{n^2+10000000n}{n^4}$ will converge

On the other hand,

$\displaystyle \sum_{n=1}^{\infty} \frac{n^3+10n}{100000n^4}$

Will diverge.

See if you can apply the rule in this situation.