Evaluate the improper integral and state what this result implies about the…

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Evaluate the improper integral

\displaystyle\int_{2}^{\infty} \frac{1}{x(\ln x)^{3}}\,dx

and state what this result implies about the convergence of the series

\displaystyle\sum_{n=2}^{\infty} \frac{1}{n(\ln n)^{3}}