Series to functions Find the function represented by the following series and find the interval of convergence of the series.
Solution 55EStep 1:In this problem we have to find the function represented by the seriesand also we have to find the interval of convergence of the series.We compute the derivative of this power series by differentiating term-by-term: (Since ) where we’ve computed the sum by summing a geometric series with common ratio , so that the last series converges whenever and diverges when . That means that the interval of convergence of the last series is (1, 1) with or without the endpoints.
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. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since the solution to 55E from 9.2 chapter was answered, more than 280 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Series, Find, functions, function, interval. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The full step-by-step solution to problem: 55E from chapter: 9.2 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. The answer to “Series to functions Find the function represented by the following series and find the interval of convergence of the series.” is broken down into a number of easy to follow steps, and 20 words.