Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 11 - Section 11.2 - Series - 11.2 Exercises: 18

Answer

Convergent 16

Work Step by Step

$4+3+\dfrac {9}{4}+\dfrac {27}{16}\ldots =\sum ^{\infty }_{k=0}4\times \left( \dfrac {3}{4}\right) ^{k}\Rightarrow \lim _{k\rightarrow \infty }4\times \left( \dfrac {3}{4}\right) ^{k}=0$ $\sum ^{\infty }_{0}4\times \left( \dfrac {3}{4}\right) ^{k}-\dfrac {a_{1}}{1-r};a_{1}=4;r=\dfrac {3}{4}\Rightarrow S_{\infty }=\dfrac {4}{1-\dfrac {3}{4}}=16$
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