   Chapter 11.2, Problem 33E

Chapter
Section
Textbook Problem

# Determine whether the series is convergent or divergent. If it is convergent, find its sum.33. ∑ n = 1 ∞ 1 4 + e − n

To determine

Whether the series is convergent or divergent and obtain the sum if the series is convergent.

Explanation

Given:

The series is n=114+en .

Here, an=14+en .

Theorem used: Series test for Divergence

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

Calculation:

Obtain the limit of the sequence (the value of the term an as n tends to infinity).

That is, compute the value of limnan=limn14+en

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