   Chapter 11.6, Problem 25E

Chapter
Section
Textbook Problem

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

To determine

Whether the series is convergent or divergent by using the root test.

Explanation

1) Concept:

Use the Root test.

2) 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, then the root test is inconclusive, that is, no conclusion can be drawn about the convergence or divergence of an.

3) Given:

n=1n2+12n2+1n

4) Calculation:

Consider n=1an=n=1n2+

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