Answer
Diverges.
Work Step by Step
The series $\Sigma_{n=1}^{\infty} n^{-0.8} $ can be written as follows
$$\Sigma_{n=1}^{\infty} \frac{1}{n^{0.8}}$$
which is p-series and since $p=0.8\lt 1$, then it diverges.
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 11 - Infinite Series - 11.5 The Ratio and Root Tests and Strategies for Choosing Tests - Exercises - Page 568: 55
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