Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 11 - Infinite Sequences and Series - 11.10 Taylor and Maclaurin Series - 11.10 Exercises - Page 811: 11


Maclaurin's series is: $\Sigma_{n=0}^{\infty}(n+1)x^{n}$ and $R=1$

Work Step by Step

$\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\frac{{(n+2)}x^{n+1}}{(n+1)x^{n}}|$ $=\lim\limits_{n \to\infty}|(\frac{n+2}{n+1}).x|$ $=|x|\lt 1$ Maclaurin's series is: $\Sigma_{n=0}^{\infty}(n+1)x^{n}$ and $R=1$
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