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Chapter 12: Q. 22 (page 838)

In Problems 22鈥�25, determine whether each infinite geometric series converges or diverges. If it converges, find its sum

3+1+13+19+......

Short Answer

Expert verified

The geometric series converges.

Its sum is:92

Step by step solution

01

Step 1. Given information

The geometric series:

3+1+13+19+.....

02

Step 2. To find common ratio and first term.

First term of the series is:a1=3

Common ratio is:13

Since common ratio of the series is less than 1.

Hence the series converges.

03

Step 3. To find sum of infinite terms.

S鈭�=31-13=323=3脳32=92

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