   Chapter 13.CR, Problem 56E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# 5 5 - 6 0 Infinite Geometric Series Determine whether the infinite geometric series is convergent or divergent. If it is convergent, find its sum. 0.1 + 0.01 + 0.001 + 0.0001 + ⋅ ⋅ ⋅

To determine

Whether the infinite geometric series 0.1+0.01+0.001+0.0001+ is convergent or divergent. Find the sum if convergent.

Explanation

Given:

The expression is given as,

0.1+0.01+0.001+0.0001+

Approach:

Check if the absolute value of the common ratio is smaller than 1.

If convergent use the formula for sum of an infinite series.

Calculation:

The common ratio is,

r=0.010.1=0.1

|r|=0.1<1.

Hence the given infinite geometric series converges

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