   Chapter 11.6, Problem 35E

Chapter
Section
Textbook Problem

# Use any test to determine whether the series is absolutely convergent, conditionally convergent, or divergent.35. ∑ n = 2 ∞ ( n ln n ) n

To determine

Whether the series is absolutely convergent or conditionally convergent or divergent.

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 or limn|an|n=  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=2(nlnn)n

Obtain the limit of |an|n

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