   Chapter 11.5, Problem 19E

Chapter
Section
Textbook Problem

# Test the series for convergence or divergence.19. ∑ n = 1 ∞ ( − 1 ) n n n n !

To determine

To test: Whether the series is convergent or divergent.

Explanation

Given:

The series is n=1(1)nnnn! .

Result used:

“If the alternating series n=1(1)n1bn=b1b2+b3b4+...   bn>0 satisfies the conditions bn+1bn   for all n and limnbn=0 , then the series is convergent; otherwise, the series is divergent.”

Calculation:

Consider the given series n=1(1)nnnn! , and bn=nnn! .

Obtain the limit of bn

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