   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 + I = 5 n + 1 4 n + 3 a n Determine whether Σ an converges or diverges.

To determine

Whether the series is converges or diverges.

Explanation

Given:

The terms of a series an are defined recursively by the equations a1=2 and an+1=5n+14n+3an.

Result used: The Ratio Test

“(i) If limn|an+1an|=L<1, then the series n=1an is absolutely convergent (and therefore convergent.)

(ii) If limn|an+1an|=L>1 or limn|an+1an|=, then the series n=1an is divergent.

(ii) If limn|an+1an|=1, the Ratio Test inconclusive; that is, no conclusion can be drawn about the convergence or divergence of n=1an.”

Calculation:

Consider the the terms of a an series are defined recursively by the equations a1=2 and an+1=5n+14n+3an

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