   Chapter 11.5, Problem 15E

Chapter
Section
Textbook Problem

# Test the series for convergence or divergence.15. ∑ n = 0 ∞ sin ( n + 1 2 ) π 1 + n

To determine

To test: Whether the series is convergent or divergent.

Explanation

Given:

The series is n=0sin(n+12)π1+n .

Result used:

“If the alternating series n=1(1)n1bn=b1b2+b3b4+...   bn>0 satisfies the conditions bn+1bn   for all n and limnbn=0 , then the series is convergent; otherwise, the series is divergent..”

Calculation:

Consider the given series n=0sin(n+12)π1+n and an=sin(n+12)π1+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

#### Solve the equations in Exercises 126. 14x2=0

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Problems 17-20, use Excel or some other technology. 17. Minimize subject to

Mathematical Applications for the Management, Life, and Social Sciences

#### In Exercises 1-22, evaluate the given expression. P(5,2)

Finite Mathematics for the Managerial, Life, and Social Sciences 