Chapter 11.4, Problem 28E

To determine

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