   Chapter 11.6, Problem 39E

Chapter
Section
Textbook Problem

The terms of a series are defined recursively by the equations a 1 = 2            a n + 1 = 5 n + 1 4 n + 3 a n Determine whether ∑ a n converges or diverges.

To determine

Whether an converges or diverges.

Explanation

1) Concept:

Use the ratio test.

2) Ratio test:

a) If limnan+1an=L<1, then the series n=1an is absolutely convergent ( and therefore convergent).

b) If limnan+1an=L>1 or limnan+1an=  then the series n=1an is divergent

c) If limnan+1an=1 then the ratio test is inconclusive

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