Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - 11.4 Absolute and Conditional Convergence - Exercises - Page 562: 1


$\sum_{n=0}^{\infty} \frac{(-1)^n}{2^n}$ converges absolutely.

Work Step by Step

We have $$\sum_{n=0}^{\infty} |\frac{(-1)^n}{2^n}|=\sum_{n=0}^{\infty} (\frac{1}{2})^n$$ which is a geometric series with $|r|=|1/2|\lt 1$, which converges. Then $\sum_{n=0}^{\infty} \frac{(-1)^n}{2^n}$ converges absolutely.
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