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.
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 10TI: Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+
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