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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q 12.54 (page 1193)

Find the sum of the infinite geometric series.
$64 + 16 + 4 + 1 + \frac{1}{4} + \frac{1}{16} + . . .$

Short Answer

Expert verified

Sum is $\frac{256}{3}$ .

Step by step solution

01

Step 1. Given information

Infinite geometric series is $64 + 16 + 4 + 1 + \frac{1}{4} + \frac{1}{16} + . . .$

02

Step 2. Find the sum of the infinite geometric series.

Consider the infinite geometric series:

$64 + 16 + 4 + 1 + \frac{1}{4} + \frac{1}{16} + . . .$

Let $a, r, S_{n}$ denote the first term, ratio of the consecutive terms and the sum.

$\begin{array}{rcl} a & = & 64 \\ r & = & \frac{16}{64} \\ = & \frac{1}{4} \\ S_{n} & = & \frac{a}{1 - r} \\ = & \frac{64}{1 - \frac{1}{4}} \\ = & \frac{64 脳 4}{3} \\ = & \frac{256}{3} \end{array}$

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Most popular questions from this chapter

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