Determine whether the series converges absolutely, conditionally or diverges?
$$\sum\limits_{n= 1}^{\infty} (-1)^{n-1} \frac{\ln(n)}{n}$$
I know that $\sum|a_{n}|$ diverges by using the comparison test:
$$\frac{\ln(n)}{n} > \frac{1}{n}$$ and the smaller, r.h.s being the divergent harmonic series.
So, should my conclusion for the alternating series be divergent or convergent conditionally*?
* How to estimate whether the alternating series terms are cancelling?