   Chapter 11.4, Problem 42E

Chapter
Section
Textbook Problem

# Give an example of a pair of series Σ an and Σ bn with positive terms where limn→∞ (an/bn) = 0 and Σ bn diverges, but Σ an converges. (Compare with Exercise 40.)

To determine

To find: An example of a pair of series an and bn with positive terms where limn(anbn)=0 and bn diverges, but an converges.

Explanation

Example:

The series n=1an=n=11n2 and n=1bn=n=11n.

Consider the series n=1an=n=11n2 and. n=1bn=n=11n

Result used:

Result used:

(1) “Suppose that an and bn are the series with positive terms,

If limn(anbn)=c where c is a finite number and, c>0 then either both series converge or both diverge.”

(2) The p-series n=11n is converges if p>1 and diverges if p1.

Calculation:

The series. n=1an=n=11n2

n<n21n2<1nn=11n2<n=11n

The series n=1bn=n=11n  must be greater than n=1an=n=11n2

### 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

#### Find the value of the sum. 29. i=1n2i

Single Variable Calculus: Early Transcendentals, Volume I

#### 23/2

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### True or False: If the three limits exist, then .

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### Define the concept of internal validity and a threat to internal validity.

Research Methods for the Behavioral Sciences (MindTap Course List) 