Chapter 11.4, Problem 27E

To determine

Whether the comparison test to be used with ${\displaystyle \sum _{k=2}^{\infty }\frac{1}{k\ln k}}$ and ${\displaystyle \sum _{k=2}^{\infty }\frac{1}{k}}$ can deduce anything about the infinite series ${\displaystyle \sum _{k=2}^{\infty }\frac{1}{k\ln k}}$.