Does this series converge absolutely or conditionally:

$\displaystyle \sum _{n=1}^\infty (-1)^n \left(\frac{1}{\ln n}\right)^4$

Problem (2): Which test do I use to see if it converges absolutely? I tried using comparison test: $\displaystyle \ln n < n \Longrightarrow \frac{1}{\ln n}>\frac{1}{n} \Longrightarrow \frac{1}{(\ln n)^4}>\frac{1}{n^4} $

$\displaystyle \frac{1}{n^4}$ converges (p-series with p>1) but this has no conclusion on whether $\displaystyle \left(\frac{1}{\ln n}\right)^4$ converges or not.