Hi, there's a really simple looking series that I don't know how to deal with.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\sum\limits_{n = 2}^\infty {\frac{{n^2 }}{{1 - n^3 }}}

[/tex]

How would I determine whether or not this series converges by using some standard convergence tests? If a_n = (n^2)/(1-n^3) then the numerator is always positive while the denominator is always negative so that a_n is always negative. So I can't think of a way to use the comparison test, limit comparison test etc. Since a_n looks like 1/n I have a feeling that the series diverges. But I can't think of any tests to use to verify whether or not my hypothesis is correct. At first I thought about using the absolute convergence test but if a series isnotabsolutely convergent, it can still be convergent so that didn't really help.

Can someone help me with this one?

Note: I would like to be able to do this without the integral test if possible.

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# Homework Help: Convergence of a very simple series

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