   Chapter 11.8, Problem 14E

Chapter
Section
Textbook Problem

# Find the radius of convergence and interval of convergence of the series.14. ∑ n = 1 ∞ x 2 n n !

To determine

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

Explanation

Given:

The series n=1x2nn! .

Ratio test:

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

Calculation:

Let an=x2nn! .

Then, an+1=x2(n+1)(n+1)! .

Obtain |an+1an| to apply the Ratio test.

|an+1an|=|x2n+2(n+1)!x2nn!|

Take limn on both sides,

limn|an+1an

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