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: 42



Work Step by Step

We are given $f(x)=\frac{2x}{1+3x}=\frac{2x}{1-(-3x)}$ for $r$ in $(-\frac{1}{3},\frac{1}{3})$ The Taylor series for $\frac{1}{1-x}$ is $1+x+x^2+x^3+...+x^n+...$ The Taylor series for $f(x)=\frac{2x}{1-(-3x)}$ is $f(x)=2x.1+2x(-3x)+2x(-3x)^2+2x(-3x)^3...+2x(-3x)^n+...$ $=2x-6x^2+18x^3-54x^4+...(-6x^{n+1})+...$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.