   Chapter 11.7, Problem 1E

Chapter
Section
Textbook Problem

# Test the series for convergence or divergence.1. ∑ n = 1 ∞ n 2 − 1 n 3 + 1

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

(2) The harmonic series n=11n is divergent.

Calculation:

Consider the series n=1an=n=1n21n3+1.

n3<n3+1n3n<n3+1n(n21)<n3+1n21n3+1<1n

Consider the series n=1bn=n=11n must be greater than n=1an=n=1n21n3+1.

Obtain the limit of anbn

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