Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 11 - Section 11.9 - Representations of Functions as Power Series - 11.9 Exercises - Page 793: 11

Answer

1-3$\Sigma\frac{(-1)^nx^n}{2^{n+1}}$

Work Step by Step

$\frac{x-1}{x+2}$ can be rewritten as = $\frac{x+2-3}{x+2}$ 1 - $\frac{3}{x+2}$ = 1 - $\frac{3}{2+x}$ 1 - $\frac{3}{2}$($\frac{1}{1+\frac{x}{2}}$) Geometric series with r=$\frac{-x}{2}$ Radius of Convergence = -2, Interval of Convergence (-2,2)
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