   Chapter 11.2, Problem 22E

Chapter
Section
Textbook Problem

# Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.22. ∑ n = 1 ∞ 5 π 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=15πn .

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=15πn .

n=15πn=5π1+5π2+5π3+=5π+5π2+5π3+

Here, the first term of the series is a=5π and the common ratio of the series is,

r

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