Determine whether the alternating series $\backslash (\backslash$sum$\_\{$n$=2\}^\{\backslash$infty$\}(-1)^\{$n$\}\backslash$frac$\{1\}\{2\backslash$ln n$\}\backslash )$ converges or diverges. Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. A$.$ The series does not satisfy the conditions of the Alternating Series Test but diverges because it is a p$-$series with p$=$ B$.$ The series does not satisfy the conditions of the Alternating Series Test but diverges by the Root Test because the limit used does not exist. C$.$ The series does not satisfy the conditions of the Alternating Series Test but converges because it is a p$-$series with p$=$ D$.$ The series converges by the Alternating Series Test. E$.$ The series does not satisfy the conditions of the Alternating Series Test but converges because it is a geometric series with $\backslash ($ r$=\backslash )$