Interval and radius of convergence Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence.
Solution 15EStep 1:In this problem we have to determine the radius of convergence of the power series.Use Ratio test to determine the radius of convergence.If and1. If L <1, converges.2. If L >1, diverges.3. If L=1, the test is inconclusive.Step 2: Consider ,= = | | = | | = | | = | |(1) = | |Step 3:The series converges for L<1.Therefore solve By using “If ”-< x < Thus the radius of convergence is .
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 15E from chapter: 9.2 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This full solution covers the following key subjects: Convergence, radius, determine, interval, power. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The answer to “Interval and radius of convergence Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence.” is broken down into a number of easy to follow steps, and 25 words. Since the solution to 15E from 9.2 chapter was answered, more than 246 students have viewed the full step-by-step answer.