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Chapter 12: Q 61. (page 825)

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

鈭�k=1鈭�123k-1

Short Answer

Expert verified

The given infinite geometric series鈭�k=1鈭�123k-1 is diverges.

Step by step solution

01

Step 1. Write the given information.

The given geometric series is:

鈭�k=1鈭�123k-1
02

Determine the first term and common ratio.

The first term isa1=12

The common ratio is the ratio of successive terms:

r=3

03

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

Ifr<1 then the infinite geometric series converges.

As we can see that 3>1, therefore the given series not converges.

The given infinite geometric series diverges.

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