Geometric series with alternating signs Evaluate the

Chapter 11, Problem 39E

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QUESTION:

35-40. Geometric series with alternating signs Evaluate the geometric series or state that it diverges.

\(\sum_{k=2}^{\infty}(-0.15)^{k}\)

Questions & Answers

QUESTION:

35-40. Geometric series with alternating signs Evaluate the geometric series or state that it diverges.

\(\sum_{k=2}^{\infty}(-0.15)^{k}\)

ANSWER:

Problem 39E

Geometric series with alternating signs Evaluate the geometric series or state that it diverges.

Solution

Step 1

In this problem we have to evaluate the geometric series  or we have to state that it diverges.

The sum of an infinite Geometric series  is given by if  .

We have  

Here and

Hence  the sum ofis

Therefore the sum of the infinite geometric series is

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