   Chapter 11.2, Problem 36E

Chapter
Section
Textbook Problem

# Determine whether the series is convergent or divergent. If it is convergent, find its sum.36. ∑ n = 1 ∞ 1 1 + ( 2 3 ) 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=111+(23)n .

Here, an=11+(23)n .

Result used:

The sequence {sn} is converges to zero when 1<s<1 .

That is, limnsn=0 if 1<s<1 .

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=limn11+(23)n

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