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: 82

Answer

converges to $k$

Work Step by Step

Formula to calculate the sum of a geometric series is: $S=\dfrac{a}{1-r}$; Consider the series $\Sigma_{n=0}^{\infty} k(\dfrac{1}{2})^{n+1}$; which shows a convergent geometric series with $a=\dfrac{k}{2}$ and common ratio $r =\dfrac{1}{2}$ $S=\dfrac{a}{1-r}=\dfrac{\dfrac{k}{2}}{1-\dfrac{1}{2}}=k$ Hence, the series converges to $k$
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