   Chapter 11.7, Problem 25E

Chapter
Section
Textbook Problem

# Test the series for convergence or divergence.25. ∑ n = 1 ∞ n ! e n 2

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=1n!en2.

Then, the (n+1) th term is, an+1=(n+1)!e(n+1)2.

Obtain the limit of |an+1an|

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