Answer
Diverges.
Work Step by Step
The series can be rewritten as:
$$
\sum_{n=1}^{\infty}\left(\frac{\pi^7}{e^8}\right)^{n}
$$
Which is a geometric series with $r=\frac{\pi^7}{e^8}\gt 1$ and hence 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 - Chapter Review Exercises - Page 592: 78
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