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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. 339 (page 1222)

In the following exercises, find the sum.
$1 - \frac{1}{5} + \frac{1}{25} - \frac{1}{125} + \frac{1}{625} - \frac{1}{3125} + . . .$

Short Answer

Expert verified

The sum is $\frac{5}{6}$ .

Step by step solution

01

Step 1. Given information.

Consider the given question,

$1 - \frac{1}{5} + \frac{1}{25} - \frac{1}{125} + \frac{1}{625} - \frac{1}{3125} + . . .$

Then,

$a_{1} = 1$

To find the common ratio,

$\frac{- \frac{1}{5}}{1} = - \frac{1}{5} r = - \frac{1}{5}$

As $|r| < 1$ , then sum of first nterms of geometric sequence,localid="1645341691527" $S = \frac{a_{1}}{1 - r} . . . . . . (i)$

02

Step 2. Find the required sum.

Substitute the values in equation (i),

$S = \frac{1}{1 - (- \frac{1}{5})} = \frac{1}{\frac{6}{5}} = \frac{5}{6}$

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Most popular questions from this chapter

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