Convergence Tests

Determinewhethertheseriessumfromn=2to∞of1(n(ln⁡n)2)convergesordiverges.Justifythechoiceoftestbeforecarryingitout.Determine whether the series sum from n = 2 to \infty of \frac{1}{(n} (\ln n)^2) converges or diverges. Justify the choice of test before carrying it out.

Start by naming the convergence test you think is most natural here, and say why it fits better than the ratio or root test.