   Chapter 11.7, Problem 32E

Chapter
Section
Textbook Problem

Test the series for convergence or divergence. ∑ n = 1 ∞ ( n ! ) n n 4 n

To determine

To test:

The series for convergence or divergence.

Explanation

1) Concept:

If an is of the form bnn, then the root test is useful.

Root Test:

If limnann=L<1, the series n=1an is absolutely convergent (and therefore convergent)

If limnann=L>1 or limnan+1an=, then series n=1an is divergent.

If limnann=1, the ratio test is inconclusive.(no conclusion)

2) Given:

n=1n!nn4n

3) Calculation:

Here,

an=n!nn4n is of the form, bnn=n!n4n where bn=n!n4

Therefore, use the root test

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