Power series from the geometric series Use the geometric I series ,for |x|<1 to determine the Maclanrin series and the interval of convergence for the following functions.
Solution 23REStep 1:In this problem we have to use the geometric series for |x|<1, to determine the Maclaurin series of and also we have to find the interval of convergenceWe have Using geometric series for |x| < 1 we get,Thus the Maclaurin series of is given by Notice that we replaced both the x in the geometric series with to get the required Maclaurin series and so we will do the same in the interval of convergence. Thus provided Thus the interval of convergence for the Maclaurin series is . That is the interval 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: 23RE from chapter: 9 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since the solution to 23RE from 9 chapter was answered, more than 278 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Series, geometric, interval, Convergence, functions. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The answer to “Power series from the geometric series Use the geometric I series ,for |x|<1 to determine the Maclanrin series and the interval of convergence for the following functions.” is broken down into a number of easy to follow steps, and 27 words.