$\sum _{ n=10 }^{ \infty }{ (-1)^ n } \frac { n^ 2 }{ ln(n) } $
How to find whether it diverges or converges
My attempt
By using alternating series test:
$\displaystyle \lim_{n \rightarrow \infty}$ $\frac { n^ 2 }{ ln(n) } $ = $\infty$.. It is not equal to zero... so the series diverges.
I don't get the reference to the alternating series test; since $(-1)^n\frac{n^2}{\log{n}}\not\to 0$, the series diverges.