   Chapter 11, Problem 18RE

Chapter
Section
Textbook Problem

# Determine whether the series is convergent or divergent.18. ∑ n = 1 ∞ n 2 n ( 1 + 2 n 2 ) 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=1n2n(1+2n2)n .

Obtain the limit of |an|n

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