Example 9. Investigate the convergence of the series $\sum_{n=2}^{\infty} \frac{1}{n \ln n}$.
Solution. We have $\int_{2}^{+\infty} \frac{d x}{x \ln x}=\left.\lim _{A \rightarrow+\infty} \ln |\ln x|\right|_{2} ^{A}=+\infty$.

Answer. The series diverges.