University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 9 - Section 9.2 - Infinite Series - Exercises - Page 498: 50

Answer

Divergent

Work Step by Step

The sum of a geometric series can be found as: $S=\dfrac{a}{1-r}$ The given series $\sum_{n=0}^{\infty} (\sqrt 2)^n$ has the first term, $a=1$, and a common ratio $r =\sqrt 2 \gt 1$ Hence, the given series $\sum_{n=0}^{\infty} (\sqrt 2)^n$ is divergent.
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