Question

\[\sum_{n=2}^{\infty} \frac{(-1)^{n+1}}{nlnn}\]

\[b_{n} = \frac{1}{nlnn}\]
\[\frac{1}{(n+1)ln(n+1)} =< \frac{1}{nlnn}\]
\[\lim_{n \rightarrow \infty} =\frac{1}{\infty} = 0\]
convergent.
is my calculation correct?