Chapter 12: Q. 22 (page 838)

In Problems 22–25, determine whether each infinite geometric series converges or diverges. If it converges, find its sum
$3 + 1 + \frac{1}{3} + \frac{1}{9} + . . . . . .$

Short Answer

Expert verified

The geometric series converges.

Its sum is: $\frac{9}{2}$

Step by step solution

Step 1. Given information

The geometric series:

$3 + 1 + \frac{1}{3} + \frac{1}{9} + . . . . .$

Step 2. To find common ratio and first term.

First term of the series is: $a_{1} = 3$

Common ratio is: $\frac{1}{3}$

Since common ratio of the series is less than 1.

Hence the series converges.

Step 3. To find sum of infinite terms.

$\begin{array}{rcl} S_{\infty} & = & \frac{3}{1 - \frac{1}{3}} \\ = & \frac{3}{\frac{2}{3}} \\ = & \frac{3 \times 3}{2} \\ = & \frac{9}{2} \end{array}$

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In Problems 22–25, determine whether each infinite geometric series converges or diverges. If it converges, find its sum
$3 + 1 + \frac{1}{3} + \frac{1}{9} + . . . . . .$

Short Answer

Step by step solution

Step 1. Given information

Step 2. To find common ratio and first term.

Step 3. To find sum of infinite terms.

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In Problems 22–25, determine whether each infinite geometric series converges or diverges. If it converges, find its sum3+1+13+19+......

Short Answer

Step by step solution

Step 1. Given information

Step 2. To find common ratio and first term.

Step 3. To find sum of infinite terms.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

In Problems 22–25, determine whether each infinite geometric series converges or diverges. If it converges, find its sum
$3 + 1 + \frac{1}{3} + \frac{1}{9} + . . . . . .$