   Chapter 11.2, Problem 32E

Chapter
Section
Textbook Problem

Determine whether the series is convergent or divergent. If it is convergent, find its sum. ∑ n = 1 ∞ [ ( − 0.2 ) n + ( 0.6 ) n − 1 ]

To determine

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

Explanation

1) Concept:

i) Geometric series:

n=1arn-1=a+ar+ar2+

is convergent, if r<1 and its sum is

n=1arn-1=a1-r  r<1

If r1, the geometric series is divergent

ii) Theorem:

If n=1an & n=1bn  are convergent series, then the series  n=1(an+bn) &

n=1(an+bn)=n=1an+n=1bn

2) Given:

n=1-0.2n+0.6n-1

3) Calculation:

Consider the given series.

n=1-0.2n+0.6n-1

By using concept (ii),

n=1-0.2n+0.6n-1=n=1(-0.2)n+n=1(0.6)n-1

n=1(-0.2)n=-0.2n=1-0.2n-1

Therefore,

n=1-0.2n+0.6n-1 =-0.2n=1-0.2n-1+n=10.6n-1

-0.2n=1-0.2n-1 & n=10

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find the mean for the following set of scores: 2, 7, 9, 4, 5, 3, 0, 6

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Find the derivatives of the functions in Problems 1-14. 10.

Mathematical Applications for the Management, Life, and Social Sciences

Evaluate limx1x31x1

Single Variable Calculus: Early Transcendentals 