Calculus with Applications (10th Edition)

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

Chapter 12 - Sequences and Series - Chapter Review - Review Exercises - Page 662: 43


$x^2-x^3+x^4-x^5+...+(-x^{n+2})...$ for $r$ in $(-1,1)$

Work Step by Step

We are given $f(x)=\frac{x^2}{x+1}=\frac{x^2}{1-(-x)}$ 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 $f(x)=\frac{x^2}{1-(-x)}$ is $f(x)=x^2.1+x^2(-x)+x^2(-x)^2+x^2(-x)^3...+x^2(-x)^n+...$ $=x^2-x^3+x^4-x^5+...+(-x^{n+2})...$
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