   Chapter 11.7, Problem 14E

Chapter
Section
Textbook Problem

# Test the series for convergence or divergence.14. ∑ n = 1 ∞ sin 2 n 1 + 2 n

To determine

To test: Whether the series convergence or divergence.

Explanation

Result used:

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

(a) If bn is convergent and anbn for all n, then an is also convergent.

(b) If bn is divergent and anbn for all n, then an is also divergent.”

(2) The geometric series n=1arn1 is convergent if |r|<1 and divergent if |r|>1.

Theorem used:

If the series an converges absolutely, then it is convergent.

Calculation:

The given series n=1an=n=1sin2n1+2n

### 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

#### 84. If , find .

Mathematical Applications for the Management, Life, and Social Sciences

#### Find f'(a). f(x)=12x

Single Variable Calculus: Early Transcendentals

#### The implied domain of is: (1, ∞) (−∞, 1) x ≠ 1 (−1, 1)

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