   Chapter 11.2, Problem 36E

Chapter
Section
Textbook Problem

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

To determine

The series is convergent or divergent and if it is convergent, find its sum.

Explanation

1) Concept:

The test of divergence of series:

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

2) Given:

n=111+23n

3) Calculation:

Consider the given series.

n=111+23n

Here an= 11+23n

By using the concept,

limnan=limn11+23n

By using the limit laws,

limnan=11+limn23n

23=0

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