   Chapter 11.2, Problem 24E

Chapter
Section
Textbook Problem

# Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.24. ∑ n = 0 ∞ 3 n + 1 ( − 2 ) n

To determine

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

Explanation

Given:

The series is n=03n+1(2)n .

Result used:

The geometric series n=1arn1 (or) a+ar+ar2+ is divergent if |r|1 , where a is the first term and r is the common ratio of the series.

Calculation:

Consider the given series n=03n+1(2)n .

n=03n+1(2)n=30+1(2)0+31+1(2)1

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