# Solution: Intervals of ConvergenceIn Exercise , (a) find the ## Problem 5E Chapter 10.7

Thomas' Calculus: Early Transcendentals | 13th Edition

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Problem 5E

Intervals of Convergence

In Exercise , (a) find the series’ radius and interval of convergence. For what values of x does the series converge (b) absolutely, (c) conditionally? Step-by-Step Solution:

Step 1 of 5</p>

Here, we have to find

The series’ radius and interval of convergence.The value of x for which the series converges absolutely.The value of x for which the series converges conditionally. .

Step 2 of 5</p>Let us use the root test in order to find the radius of convergence.

Therefore, according to the ratio test, a series is said to be absolutely convergent if …..(1) Therefore, according to our question, we have .

Thus,  Thus, using (1), we have  …..(2)  .

Therefore, from (2) we get the radius of convergence as 10 and the centre as .

Step 3 of 5</p>

Now let us test the convergence of the series at the endpoints.

At , we have the series as .

This is a Divergent Geometric series with and such that .

At , we have the series as .

We know that the infinite sum of any non zero constant diverges.

Therefore, the series diverges.

Step 4 of 5

Step 5 of 5

##### ISBN: 9780321884077

Since the solution to 5E from 10.7 chapter was answered, more than 240 students have viewed the full step-by-step answer. The answer to “Intervals of ConvergenceIn Exercise , (a) find the series’ radius and interval of convergence. For what values of x does the series converge (b) absolutely, (c) conditionally?” is broken down into a number of easy to follow steps, and 27 words. This full solution covers the following key subjects: Convergence, Series, ind, absolutely, exercise. This expansive textbook survival guide covers 138 chapters, and 9198 solutions. Thomas' Calculus: Early Transcendentals was written by Sieva Kozinsky and is associated to the ISBN: 9780321884077. This textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13th. The full step-by-step solution to problem: 5E from chapter: 10.7 was answered by Sieva Kozinsky, our top Calculus solution expert on 08/01/17, 02:37PM.

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