   Chapter 11.2, Problem 37E

Chapter
Section
Textbook Problem

Determine whether the series is convergent or divergent. If it is convergent, find its sum. ∑ n = 1 ∞ ln n 2 + 1 2 n 2 + 1

To determine

The series is convergent or divergent and if it is convergent, find its sum.

Explanation

1) Concept:

Test of divergence of series:

If limnan  does not exist or if limnan0,   then the series n=1an  is divergent.

2) Given:

n=1lnn2+12n2+1

3) Calculation:

Consider the given series.

n=1lnn2+12n2+1

Here,an=lnn2+12n2+1

By using the concept, find limnan

limnan=limnlnn2+12n2+1

Dividing the numerator and the denominator by the highest power of n  in the denominator, that is, by n2

limnan=limn̼

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