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: 62

Answer

First four terms: $1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}$ Sum: $S_\infty = 2$

Work Step by Step

The next term is the previous term multiplied by a factor of $\frac{1}{2}$. The first four terms are given in the problem: $1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}$ The infinite series is a geometric sequence with the an initial term of $a_0 = 1$ and a factor of $r = \frac{1}{2}$, where $r<1$. $S_\infty = \frac{a_0}{1-r} = \frac{1}{1- \frac{1}{2}} = 2$
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