   Chapter 11.2, Problem 47E

Chapter
Section
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

Find more solutions based on key concepts 