Answer
Converges.
Work Step by Step
We have the series
$$
\sum_{n=1}^{\infty}\left(\frac{2}{3}\right)^{n}
$$
which is a geometric series with $r=2/3\lt 1$ and hence the series converges.
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: 77
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