Chapter 11.2, Problem 36E

### Single Variable Calculus

8th Edition
James Stewart
ISBN: 9781305266636

Chapter
Section

### Single Variable Calculus

8th Edition
James Stewart
ISBN: 9781305266636
Textbook Problem

# Determine whether the series is convergent or divergent. If it is convergent, find its sum.36. ∑ n = 1 ∞ 1 1 + ( 2 3 ) n

To determine

Whether the series is convergent or divergent and obtain the sum if the series is convergent.

Explanation

Given:

The series is âˆ‘n=1âˆž11+(23)n .

Here, an=11+(23)n .

Result used:

The sequence {sn} is converges to zero when âˆ’1<s<1 .

That is, limnâ†’âˆžsn=0Â ifÂ âˆ’1<s<1 .

Theorem used: Series test for Divergence

If limnâ†’âˆžan does not exist or limnâ†’âˆžanâ‰ 0 , then the series âˆ‘n=1âˆžan is divergent.

Calculation:

Obtain the limit of the sequence (the value of the term an as n tends to infinity).

That is, compute the value of limnâ†’âˆžan=limnâ†’âˆž11+(23)n

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started