   Chapter 11.7, Problem 17E

Chapter
Section
Textbook Problem

# Test the series for convergence or divergence.17. ∑ n = 1 ∞ 1 ⋅ 3 ⋅ 5 ⋅ ⋯ ⋅ ( 2 n − 1 ) 2 ⋅ 5 ⋅ 8 ⋅ ⋯ ⋅ ( 3 n − 1 )

To determine

To test: Whether the series convergence or divergence.

Explanation

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, then the Ratio Test is inconclusive; that is, no conclusion can be drawn about the convergence or divergence of n=1an.

Calculation:

The given series n=1an=n=1135(2n1)258(3n1), where an=135(2n1)258(3n1).

Then, the (n+1) th term is,

an+1=135(2(n+1)1)258(3(n+1)1)an+1=135(2n1)(2n+1)258(3n1)(3n+2)

Obtain the limit of |an+1an|

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