Algebra and Trigonometry 10th Edition

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

Chapter 11 - 11.1 - Sequences and Series - 11.1 Exercises - Page 778: 84


$\displaystyle \sum_{i=0}^{7}(-1)^i\frac{1}{2^i}$

Work Step by Step

$1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+\frac{1}{16}-\frac{1}{32}+\frac{1}{64}-\frac{1}{128}=(-1)^0\frac{1}{2^0}+(-1)^1\frac{1}{2^1}+(-1)^2\frac{1}{2^2}+(-1)^3\frac{1}{2^3}+(-1)^4\frac{1}{2^4}+(-1)^5\frac{1}{2^5}+(-1)^6\frac{1}{2^6}+(-1)^7\frac{1}{2^7}=\displaystyle \sum_{i=0}^{7}(-1)^i\frac{1}{2^i}$
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