(2) Let y = Σanz". (a) Compute y and y" and write out the first four terms of the series, as well as the coefficient of z" in the general term. (b) Show that if y"=y, then the coefficients ag and a, are arbitrary, and determine a, and as in terms of do and a. (e) Show that 12- (d) From (2c), show that a a (n+2)(n+1) do for n = 0, 1, 2, 3, ..... for n 0, 2, 4,... and da a₂ n! for n=1,3,5,....

(2) Let y = Σanz". (a) Compute y and y" and write out the first four terms of the series, as well as the coefficient of z" in the general term. (b) Show that if y"=y, then the coefficients ag and a, are arbitrary, and determine a, and as in terms of do and a. (e) Show that 12- (d) From (2c), show that a a (n+2)(n+1) do for n = 0, 1, 2, 3, ..... for n 0, 2, 4,... and da a₂ n! for n=1,3,5,....

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 68E

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