   Chapter 11.7, Problem 6E

Chapter
Section
Textbook Problem

# Test the series for convergence or divergence.6. ∑ n = 1 ∞ n 2 n ( 1 + n ) 3 n

To determine

To test: Whether the series convergence or divergence.

Explanation

Result used: The Root Test

(i) If limn|an|n=L<1, then the series n=1an is absolutely convergent (and therefore convergent).

(ii) If limn|an|n=L>1, then the series n=1an is divergent.

(iii) If limn|an|n=1, the Root Test is inconclusive.

Calculation:

The given series n=1an=n=1n2n(1+n)3n.

Obtain the limit of |an|n.

limn|an|n=limn[|n2n(1+n)3n|<

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