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Chapter 12: Q 57. (page 825)

In Problems 51鈥�66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.

8+12+18+27+....

Short Answer

Expert verified

The given infinite geometric series 8+12+18+27+....is diverges.

Step by step solution

01

Step 1. Write the given information.

The given geometric series is:

8+12+18+27+....

02

Find the common ratio.

a1=8,a2=12,a3=18,a4=27

The common ratio is the ratio of successive terms:

128=32,1812=32r=32

03

Step 3. Determine whether the infinite geometric series is converges or diverges.

If r<1then the infinite geometric series converges.

As we can see that r=32and32>1, therefore the given series is not convergent.

The given infinite geometric series is diverges.

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