Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 11 - 11.3 - Geometric Sequences and Series - 11.3 Exercises - Page 796: 69



Work Step by Step

$\displaystyle \sum_{n=0}^{∞}(\frac{1}{2})^n=(\frac{1}{2})^0+(\frac{1}{2})^1+(\frac{1}{2})^2+...$ $a_1=(\frac{1}{2})^0=1$ $r=\frac{a_2}{a_1}=\frac{(\frac{1}{2})^1}{(\frac{1}{2})^0}=\frac{1}{2}$ $S=\frac{a_1}{1-r}=\frac{1}{1-\frac{1}{2}}=2$
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