   Chapter 11.8, Problem 23E

Chapter
Section
Textbook Problem

# Find the radius of convergence and interval of convergence of the series.23. ∑ n = 1 ∞ n ! ( 2 x − 1 ) n

To determine

To find: The radius of convergence and interval of convergence of the series.

Explanation

Given:

The series is n=1n!(2x1)n .

Ratio test:

If limn|an+1an|=L<1 , then the series n=1an is absolutely convergent.

Calculation:

Let an=n!(2x1)n .

Then, an+1=(n+1)!(2x1)n+1 .

Obtain |an+1an| .

|an+1an|=|(n+1)!(2x1)n+1n!(2x1)n|

Take limn on both sides,

limn|

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