   Chapter 11.4, Problem 15E

Chapter
Section
Textbook Problem

Determine whether the series converges or diverges. ∑ n = 1 ∞ 4 n + 1 3 n − 2

To determine

The series n=14n+13n-2 converges or diverges.

Explanation

1) Concept:

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

ii) A geometric series [arn-1 converges if r<1 and diverges if r1]

2) Formula:

an and bn are series with positive terms

(i) If bn is convergent and anbn for all n, then an is also convergent.

(ii) If bn is divergent and anbn for all n, then an is also divergent.

3) Given:

n=14n+13n-2

4) Calculation:

Let

an=4n+13n-2

To choose bn

3n-</

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