   Chapter 11.6, Problem 32E

Chapter
Section
Textbook Problem

# Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent.32. ∑ n = 1 ∞ ( 1 − n 2 + 3 n ) n

To determine

Whether the series is absolutely convergent or conditionally convergent or divergent.

Explanation

Result used: The Root Test

(i) If limn|an|n=L<1, then the series n=1an is absolutely convergent (and therefore convergent).

(ii) If limn|an|n=L>1 or limn|an|n=  then the series n=1an is divergent.

(iii) If limn|an|n=1, the Root Test is inconclusive.”

Calculation:

The given series n=1an=n=1(1n2+3n)n.

Here an=(1n2+3n)n.

Obtain the limit of |an|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

#### In problems 27-30, find. 27.

Mathematical Applications for the Management, Life, and Social Sciences

#### In Exercises 116, determine whether the argument is valid. pq~pq

Finite Mathematics for the Managerial, Life, and Social Sciences

#### What is the integrating factor for xy′ + 6x2y = 10 − x3?

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

Mathematics For Machine Technology 