Intervals of ConvergenceIn Exercise , (a) find | Ch 10.7 - 6E

Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass

Problem 6E Chapter 10.7

Thomas' Calculus: Early Transcendentals | 13th Edition

  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass

Thomas' Calculus: Early Transcendentals | 13th Edition

4 5 0 356 Reviews
10
0
Problem 6E

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 have

We get the interval of convergence from (2) as .

Therefore, we get the radius of convergence as  and the center is .

Step 3 of 5</p>

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

At , we have the series as

, is diverging geometric series..

At , we have the series as

, is a divergent series.

Step 4 of 5

Chapter 10.7, Problem 6E is Solved
Step 5 of 5

Textbook: Thomas' Calculus: Early Transcendentals
Edition: 13th
Author: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass
ISBN: 9780321884077

×
Log in to StudySoup
Get Full Access to Thomas' Calculus: Early Transcendentals - 13th Edition - Chapter 10.7 - Problem 6e

Forgot password? Reset password here

Join StudySoup for FREE
Get Full Access to Thomas' Calculus: Early Transcendentals - 13th Edition - Chapter 10.7 - Problem 6e
Join with Email
Already have an account? Login here
Reset your password

I don't want to reset my password

Need help? Contact support

Need an Account? Is not associated with an account
Sign up
We're here to help

Having trouble accessing your account? Let us help you, contact support at +1(510) 944-1054 or support@studysoup.com

Got it, thanks!
Password Reset Request Sent An email has been sent to the email address associated to your account. Follow the link in the email to reset your password. If you're having trouble finding our email please check your spam folder
Got it, thanks!
Already have an Account? Is already in use
Log in
Incorrect Password The password used to log in with this account is incorrect
Try Again

Forgot password? Reset it here