   Chapter 11.4, Problem 23E

Chapter
Section
Textbook Problem

# Determine whether the series converges or diverges.23. ∑ n = 1 ∞ 5 + 2 n ( 1 + n 2 ) 2

To determine

Whether the series n=15+2n(1+n2)2 is convergent or not.

Explanation

Formula used:

Limit comparison test:

Suppose that 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.

Calculation:

Suppose that an=5+2n(1+n2)2 and bn=1n3.

Calculate limnanbn as follows.

limnanbn=limn5+2n(1+n2)21n3=limnn3(5+2n)(1+n2)2=limn5n3+2n4

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