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Chapter 12: Q 174. (page 1199)

In the following exercises, find the sum of each infinite geometric series.

5+15+45+135+405+1215+鈥�

Short Answer

Expert verified

The sum does not exist.

Step by step solution

01

Step 1. Given Information.

Consider the given series:

6+12+24+48+96+192+鈰�

02

Step 2. Find the common ratio.

To find the common ratio, divide the second term by first.

r=155=3

And the ratio isr>1.

03

Step 3. Find the sum of infinite series. 

  • Since the value of r is 3.
  • Two is greater than one.
  • Thus, the sum of the given sequence does not exist.

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