Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 12 - Sequences and Series - 12.5 Taylor Series - 12.5 Exercises - Page 647: 17



Work Step by Step

We are given $f(x)=\frac{2}{1+x^2}=\frac{2}{1-(-x^2)}$ for $r$ in $(-1,1)$ The Taylor series for $\frac{1}{1-x}$ is $1+x+x^2+x^3+...+x^n+...$ The Taylor series for $f(x)=\frac{2}{1-(-x^2)}$ is $f(x)=2.1+2(-x^2)+2(-x^2)^2+2(-x^2)^3...+2(-x^2)^n+...$ $=2-2x^2+2x^4-2x^6+...+2(-x^{2n})+...$
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