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Begin with the Maclaurin (Taylor) series: cos r = 1 - 2! 4! 6! (a) Evaluate cos 0. (b) List the zeros of cos r. (c) Expand cos r as an infinite product in the form Pla) = (1 - ) (1 - #) (1 -). where a, b, c, ... are the zeros of cos r.

Begin with the Maclaurin (Taylor) series: cos r = 1 - 2! 4! 6! (a) Evaluate cos 0. (b) List the zeros of cos r. (c) Expand cos r as an infinite product in the form Pla) = (1 - ) (1 - #) (1 -). where a, b, c, ... are the zeros of cos r.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 74E
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Begin with the Maclaurin (Taylor) series: cos r = 1 – 2! 4! 6! (a) Evaluate cos 0. (b) List the zeros of cos r. (c) Expand cos r as an infinite product in the form P(2) = (1 - 4) (1 - #) (1 - ).-- where a, b, c,... are the zeros of cos r. (d) Equate the coefficients of the quadratic term in the Taylor expansion of cos r to the corresponding coefficient in the infinite product representa- tion of cos r obtained in part (c). (e) Use the result in part (d) above to derive the sum of the reciprocals of the squares of the odd integers: 1 1 + 9. 1+ + 81 + 25 49
Transcribed Image Text:Begin with the Maclaurin (Taylor) series: cos r = 1 – 2! 4! 6! (a) Evaluate cos 0. (b) List the zeros of cos r. (c) Expand cos r as an infinite product in the form P(2) = (1 - 4) (1 - #) (1 - ).-- where a, b, c,... are the zeros of cos r. (d) Equate the coefficients of the quadratic term in the Taylor expansion of cos r to the corresponding coefficient in the infinite product representa- tion of cos r obtained in part (c). (e) Use the result in part (d) above to derive the sum of the reciprocals of the squares of the odd integers: 1 1 + 9. 1+ + 81 + 25 49
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Kindly answer parts d and e too . I need answer as soon as possible

Begin with the Maclaurin (Taylor) series: x² 2-6 - cos .r = 1. 2! 4! 6! (a) Evaluate cos 0. (b) List the zeros of cos r. (c) Expand cos e as an infinite product in the form P(x) = (1 - ) (¹ - ) (¹-2)... where a, b, c, ... are the zeros of cos.z. (d) Equate the coefficients of the quadratic term in the Taylor expansion of cos r to the corresponding coefficient in the infinite product representa- tion of cos z obtained in part (c). (e) Use the result in part (d) above to derive the sum of the reciprocals of the squares of the odd integers: 1 1 1+ + + + 9 25 49 + 앗 100 11
Transcribed Image Text:Begin with the Maclaurin (Taylor) series: x² 2-6 - cos .r = 1. 2! 4! 6! (a) Evaluate cos 0. (b) List the zeros of cos r. (c) Expand cos e as an infinite product in the form P(x) = (1 - ) (¹ - ) (¹-2)... where a, b, c, ... are the zeros of cos.z. (d) Equate the coefficients of the quadratic term in the Taylor expansion of cos r to the corresponding coefficient in the infinite product representa- tion of cos z obtained in part (c). (e) Use the result in part (d) above to derive the sum of the reciprocals of the squares of the odd integers: 1 1 1+ + + + 9 25 49 + 앗 100 11
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