Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 11 - Infinite Sequences and Series - 11.9 Exercises - Page 776: 19

Answer

$\sum_{n=0}^{\infty}(2n+1)x^{n}$, $R=1$

Work Step by Step

$f(x)=\frac{1+x}{(1-x)^{2}}=\sum_{n=0}^{\infty}(2n+1)x^{n}$ $\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\frac{(2(n+1)+1)x^{n+1}}{(2n+1)x^{n}}|$ $=|x|\lt 1$ The given series converges with $R=1$
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