Chapter 8.4, Problem 58E

Log p-series Consider the series ${\displaystyle \underset{k=2}{\overset{\ne }{\sum }}\frac{1}{k{(\ln k)}^p}}$, where p is a real number.

1. a. Use the Integral Test to determine the values of p for which this series converges.
2. b. Does this series converge faster for p = 2 or p = 3? Explain.