Answer
Converges for p>1
Work Step by Step
Factoring out the constant $ \frac{1}{k(\ln k)^p}$ leaves
$$\Sigma^m_{k=1} \frac{1}{k(\ln k)^p}$$
This is a p-series with p>1, so it converges.
Calculus, 10th Edition (Anton)
by Anton, Howard
Published by
Wiley
ISBN 10:
0-47064-772-8
ISBN 13:
978-0-47064-772-1
Chapter 9 - Infinite Series - 9.4 Convergence Tests - Exercises Set 9.4 - Page 629: 25
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