   Chapter 11.7, Problem 29E

Chapter
Section
Textbook Problem

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

To determine

To test:

The series for convergence or divergence.

Explanation

1) Concept:

If the series is of the form -1n-1bn or -1nbn, then the alternating series test is an obvious possibility.

Alternating series test:

If the alternating series

n=1-1nbn=b1-b2+b3-b4+       bn>0

satisfies

(i) bn+1bn for all n

(ii) limnbn=0

then the series is convergent.

2) Given:

n=1-1ncoshn

3) Calculation:

The given series is of the form -1nbn

where bn=1coshn>0 is the alternating series

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