Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 10: Infinite Sequences and Series - Section 10.2 - Infinite Series - Exercises 10.2 - Page 580: 78


converges to $\dfrac{1}{1-\ln x}$ for $|\ln x| \lt 1$ or, $e^{-1} \lt x \lt e$

Work Step by Step

Formula to calculate the sum of a geometric series is: $S=\dfrac{a}{1-r}$; Here, $a=1$ and common ratio $r =\ln x$ $S=\dfrac{a}{1-r}=\dfrac{1}{(1-\ln x)}$ Hence, the series converges to $\dfrac{1}{(1-\ln x)}$ for $|\ln x| \lt 1$ or, $e^{-1} \lt x \lt e$
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