   Chapter 11.4, Problem 23E

Chapter
Section
Textbook Problem

Determine whether the series converges or diverges. ∑ n − 1 ∞ 5 + 2 n ( 1 + n 2 ) 2

To determine

The series n=15+2n1+n22 converges or diverges.

Explanation

1) Concept:

i) Use the limit comparison test to determine whether the series converges or diverges

ii) A p-series [ 1/np converges if p>1 and diverges if p1]

2) Formula:

Limit Comparison Test:

an and bn are series with positive terms

If limnanbn=c where c is a finite number and c>0, then either both series converge or both diverge

3) Given:

n=15+2n1+n22

4) Calculation:

Let

an=5+2n1+n22

bn=1n3

limnanbn=limnn35+2n1+n22

Divide the numerator and denominator by n4

=limn5n3+2n<

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