Recall that the radius of convergence R of a power series with coefficients a, is found by first computing An+1 L = lim an and then computing R L' subject to the convention that if L = 0, then R = x and if L = o, then R = 0. Consider the two power series (-1)" and (-1)- (*- 2)" n=1 n=1 (1) Compute the radius of convergence of each series. (2) Does the first series converge when r = 1/2? Does the second series converge with r 1/2? Provide a brief justification for your answer based on the result of the previous item. (3) Determine the interval of convergence of the first series.
Recall that the radius of convergence R of a power series with coefficients a, is found by first computing An+1 L = lim an and then computing R L' subject to the convention that if L = 0, then R = x and if L = o, then R = 0. Consider the two power series (-1)" and (-1)- (*- 2)" n=1 n=1 (1) Compute the radius of convergence of each series. (2) Does the first series converge when r = 1/2? Does the second series converge with r 1/2? Provide a brief justification for your answer based on the result of the previous item. (3) Determine the interval of convergence of the first series.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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