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In 1–4 find the radius of convergence and interval of

A First Course in Differential Equations with Modeling Applications | 10th Edition | ISBN: 9781111827052 | Authors: Dennis G. Zill ISBN: 9781111827052 44

Solution for problem 3E Chapter 6.1

A First Course in Differential Equations with Modeling Applications | 10th Edition

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A First Course in Differential Equations with Modeling Applications | 10th Edition | ISBN: 9781111827052 | Authors: Dennis G. Zill

A First Course in Differential Equations with Modeling Applications | 10th Edition

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Problem 3E

In Problems 1–4 find the radius of convergence and interval of convergence for the given power series.

Step-by-Step Solution:

Step 1</p>

In this problem, we are asked to find the interval and the radius of convergence for the power series.

Step 2</p>

To find the Radius of convergence, let us use the ratio test.

Therefore

Thus for  the series converges.

Therefore the radius of convergence is .

Step 3</p>

Now we have to find the interval of convergence.

For that, we have to check whether the series is convergent at the endpoints  and .

Therefore at the series becomes

 

This the series diverges at , by the  p series test.

Step 4 of 5

Chapter 6.1, Problem 3E is Solved
Step 5 of 5

Textbook: A First Course in Differential Equations with Modeling Applications
Edition: 10
Author: Dennis G. Zill
ISBN: 9781111827052

The full step-by-step solution to problem: 3E from chapter: 6.1 was answered by , our top Calculus solution expert on 07/17/17, 09:41AM. The answer to “In 1–4 find the radius of convergence and interval of convergence for the given power series.” is broken down into a number of easy to follow steps, and 16 words. A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052. This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. Since the solution to 3E from 6.1 chapter was answered, more than 257 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Convergence, interval, given, Find, power. This expansive textbook survival guide covers 109 chapters, and 4053 solutions.

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In 1–4 find the radius of convergence and interval of

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