   Chapter 11.7, Problem 21E

Chapter
Section
Textbook Problem

Test the series for convergence or divergence. ∑ n = 1 ∞ ( − 1 ) n cos ( 1 / n 2 )

To determine

To test:

The series for convergence or divergence.

Explanation

1) Concept:

limnan0, then the test for divergence should be used.

Test for Divergence:

If limnan does not exist or if limnan0, then the series n=1an is divergent.

2) Given:

n=1-1ncos1n2

3) Calculation:

Here,

an=-1ncos1n2

Then,

limnan

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