   Chapter 11.2, Problem 23E

Chapter
Section
Textbook Problem

# Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.23. ∑ n = 1 ∞ ( − 3 ) n − 1 4 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=1(3)n14n .

Result used:

The geometric series n=1arn1 (or) a+ar+ar2+ is convergent if |r|<1 and its sum is a1r , where a is the first term and r is the common ratio of the series.

Calculation:

Consider the given series n=1(3)n14n .

n=1(3)n14n=(3)1141+(3)2142+(3)3143+(3)4144+=(3)04+(3)142+(3)243+(3)344+

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