# Intervals of ConvergenceIn Exercise , (a) | Ch 10.7 - 19E ## Problem 19E Chapter 10.7

Thomas' Calculus: Early Transcendentals | 13th Edition

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Problem 19E

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 ratio 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, we get the radius of convergence as 3 and the centre as .

Using (2), we can write the interval of convergence as .

Step 3 of 5</p>

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

At , we have the series as .

Now, using the nth term test for divergence, we can see that .

Therefore, the series diverges.

At , we have the series as .

Now, using the nth term test for divergence, we can see that .

Therefore, the series diverges.

Thus, we can see that the series does not converge conditionally for any value of x.

Step 4 of 5

Step 5 of 5

##### ISBN: 9780321884077

Thomas' Calculus: Early Transcendentals was written by Sieva Kozinsky and is associated to the ISBN: 9780321884077. Since the solution to 19E from 10.7 chapter was answered, more than 229 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. The full step-by-step solution to problem: 19E from chapter: 10.7 was answered by Sieva Kozinsky, our top Calculus solution expert on 08/01/17, 02:37PM. This textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13th. This full solution covers the following key subjects: Convergence, Series, ind, absolutely, exercise. This expansive textbook survival guide covers 138 chapters, and 9198 solutions.

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