   Chapter 11.5, Problem 6E

Chapter
Section
Textbook Problem

Test the series for convergence or divergence. ∑ n = 0 ∞ ( − 1 ) n + 1 n + 1

To determine

To test:

The given series is convergent or divergent

Explanation

1) Concept:

The Alternating Series Test:

If the alternating series

n=1-1n-1bn=b1-b2+b3-b4+b5-b6+, bn>0

satisfies,

i. bn+1<bn,  for all n

ii. limnbn=0

then the series is convergent

2) Given:

n=1-1n+1n+1

3) Calculation:

The given series is an alternating series and it can be written as

n=1-1n+1n+1=n=1-1n+1b

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

Differentiate. y = sec tan

Calculus: Early Transcendentals

Solve the equations in Exercises 126. x4x+1xx1=0

Finite Mathematics and Applied Calculus (MindTap Course List)

Define the terms population and sample, and explain the role of each in a research study.

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

In Exercises 14, find the values of x that satisfy the inequality (inequalities). 2. 2 3x + 1 7

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

Proof Prove that aN=vav.

Calculus: Early Transcendental Functions (MindTap Course List) 