Calculus (3rd Edition)

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

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.
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