Chapter 11.2, Problem 47E

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

Chapter
Section

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Determine whether the series is convergent or divergent by expressing s n as a telescoping sum (as in Example 8). If it is convergent, find its sum. ∑ n = 1 ∞ ( e 1 n − e 1 n + 1 )

To determine

The series is convergent or divergent by expressing sn as a telescoping sum and if it is convergent, find its sum.

Explanation

1) Concept:

Use definition to determine whether the series is convergent or divergent by expressing sn as telescoping sum and find the sum of series.

2) Definition:

A series n=1an=a1+a2+a3+, let sn denote its nth partial sum

sn=i=1nai=a1+a2+a3++an

If the sequence {sn} is convergent and limnsn=s exists as a real number, then the series an is called convergent and written as

a1+a2+a3++an+=s

The number s is called the sum of the series.

If the sequence {sn} is divergent, then the series an is called divergent.

3) Given:

n=1e1n-e1(n+1)

4) Calculation:

Consider

n=1e1n-e1(n+1)

The partial sums are

sn=i=1n

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