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: 91


(a) $-\frac{3}{2}$ (b) $-\frac{5}{4}$ (c) $-\frac{11}{8}$

Work Step by Step

$\displaystyle \sum_{n=1}^{∞}4(-\frac{1}{2})^n$ (a) $4(-\frac{1}{2})^1+4(-\frac{1}{2})^2+4(-\frac{1}{2})^3=-2+1-\frac{1}{2}=-\frac{3}{2}$ (b) $4(-\frac{1}{2})^1+4(-\frac{1}{2})^2+4(-\frac{1}{2})^3+4(-\frac{1}{2})^4=-2+1-\frac{1}{2}+\frac{1}{4}=-\frac{5}{4}$ (c) $4(-\frac{1}{2})^1+4(-\frac{1}{2})^2+4(-\frac{1}{2})^3+4(-\frac{1}{2})^4+4(-\frac{1}{2})^5=-2+1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}=-\frac{11}{8}$
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