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: 5



Work Step by Step

We are given $f(x)=\frac{5}{2-x}=\frac{\frac{5}{2}}{1-\frac{x}{2}}=\frac{5}{2}\frac{1}{1-\frac{x}{2}}$ with $c=\frac{5}{2}$ for $r$ in $(-2,2)$ The Taylor series for $f(x)=\frac{5}{2-x}$ is $f(x)=\frac{5}{2}.1+\frac{5}{2}(\frac{x}{2})+\frac{5}{2}(\frac{x}{2})^{2}+\frac{5}{2}(\frac{x}{2})^{3}...+\frac{5}{2}(\frac{x}{2})^n+...$ $=\frac{5}{2}+\frac{5x}{4}+\frac{5x^2}{8}+\frac{5x^3}{16}+...+\frac{5x^n}{2^{n+1}}+...$
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