Calculus: Early Transcendentals (2nd Edition)

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

Chapter 8 - Sequences and Infinite Series - 8.1 An Overview - 8.1 Exercises: 60

Answer

First four terms: $0.6, 0.06, 0.006, 0.0006$ Sum: $S_\infty = \frac{2}{3}$

Work Step by Step

Each subsequent term is the previous term multiplied by a factor of $0.1$. $a_1 = 0.6$ $a_2 = 0.06$ $a_3 = 0.006$ $a_4 = 0.0006$ The infinite series is a geometric sequence with a common ratio of $r = 0.1$, which is less than $1$. Given the first term of a series, $a_1$, and a common ratio $r$ that's less than $1$, the sum is given by $Sum: S_\infty = \frac{a_1}{1-r}$ Sum: $S_\infty = \frac{0.6}{1-0.1} = \frac{2}{3}$
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