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 10EStep 1:Given series is and To determine the radius of convergence we use ratio test which states: The ratio test states that:a. If then the series convergesb. If then the series divergesc. If or the limit does not exist then the test is inconclusive.Calculating L, we get Series converge, if . Using this we writeSo, the radius of convergence for this power series is R=5.
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
This full solution covers the following key subjects: Convergence, radius, determine, interval, power. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The full step-by-step solution to problem: 10E from chapter: 9.2 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 10E from 9.2 chapter was answered, more than 275 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. 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.