   Chapter 11.6, Problem 28E

Chapter
Section
Textbook Problem

# Use the Root Test to determine whether the series is convergent or divergent.28. ∑ n = 1 ∞ ( − 2 n n + 1 ) 5 n

To determine

Whether the series is 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=1(2nn+1)5n

Here, an=(2nn+1)5n.

Obtain the limit of |an|n.

limn|an|n=limn[|(2nn+1)5n|1n]</

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