   Chapter 11, Problem 26RE

Chapter
Section
Textbook Problem

# Determine whether the series is conditionally convergent, absolutely convergent, or divergent.26. ∑ n = 2 ∞ ( − 1 ) n n ln   n

To determine

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

Explanation

Result used: Alternating Series Test

“If the alternating series n=1(1)n1bn=b1b2+b3b4+...   bn>0 satisfies, (i) bn+1bn   for all n and (ii) limnbn=0 , then the series is convergent. Otherwise it is divergent.

Calculation:

Consider the series n=2an=n=2(1)nnlnn where bn=nlnn

Obtain the limnbn

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