Chapter 11.4, Problem 13E

### Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

Chapter
Section

### Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

# Determine whether the series converges or diverges.13. ∑ n = 1 ∞ 1 + cos n e n

To determine

Whether the series n=11+cosnen converges or diverges.

Explanation

Given:

The series is n=11+cosnen .

Result used:

(1) “Suppose that an and bn are the series with positive terms,

(a) If bn is convergent and anbn for all n , then an is also convergent.

(b) If bn is divergent and anbn for all n , then an is also divergent.”

(2) The geometric series n=1arn1 is convergent if |r|<1 and divergent if |r|>1 .

Calculation:

Consider the given series n=11+cosnen

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