Test the Following Series for Convergence or Divergence $\sum _ { n = 2 } ^ { \infty } \frac { ( - 1 ) ^ { n - 1 } } { n \ln n }$

Test the following series for convergence or divergence: $\sum _ { n = 2 } ^ { \infty } \frac { ( - 1 ) ^ { n - 1 } } { n \ln n }$ .