Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 8 - Sequences and Infinite Series - 8.3 Infinite Series - 8.3 Exercises: 8

Answer

$1\times \dfrac {\left( \left( \dfrac {1}{4}\right) ^{11}-1\right) }{\dfrac {1}{4}-1}=\dfrac {1398101}{1048576}$

Work Step by Step

$\sum ^{10}_{k=0}\left( \dfrac {1}{4}\right) ^{k}=\dfrac {a_{1}\left( r^{n}-1\right) }{r-1};a_{1}=\left( \dfrac {1}{4}\right) ^{0}=1;r=\dfrac {1}{4};n=11\Rightarrow S_{n}=1\times \dfrac {\left( \left( \dfrac {1}{4}\right) ^{11}-1\right) }{\dfrac {1}{4}-1}=\dfrac {1398101}{1048576}$
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