Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(-1)"r2n 1. For all z € R, cos I = L(2n)! -Σ n=0 (a) Find a power series that is equal to r cos(a) for all r ER. (b) Differentiate the series in (la) to find a power series that is equal to cos(r²) – 212 sin(r?) for all a E R. (c) Use the result in (1b) to prove that (-16)"(4n + 1) (2n)! cos(4) – 8 sin(4). n=0

(-1)"r2n 1. For all z € R, cos I = L(2n)! -Σ n=0 (a) Find a power series that is equal to r cos(a) for all r ER. (b) Differentiate the series in (la) to find a power series that is equal to cos(r²) – 212 sin(r?) for all a E R. (c) Use the result in (1b) to prove that (-16)"(4n + 1) (2n)! cos(4) – 8 sin(4). n=0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
See similar textbooks
icon
Related questions
Question
100%
+00 (-1)"2n (2n)! 1. For all x € R, cos a = n=0 (a) Find a power series that is equal to x cos(x2) for all a E R. (b) Differentiate the series in (la) to find a power series that is equal to cos(x2) – 2x2 sin(x2) for all a eR. (c) Use the result in (1b) to prove that +oo (-16)" (4n + 1) (2n)! = cos(4) – 8 sin(4). n=0
Transcribed Image Text:+00 (-1)"2n (2n)! 1. For all x € R, cos a = n=0 (a) Find a power series that is equal to x cos(x2) for all a E R. (b) Differentiate the series in (la) to find a power series that is equal to cos(x2) – 2x2 sin(x2) for all a eR. (c) Use the result in (1b) to prove that +oo (-16)" (4n + 1) (2n)! = cos(4) – 8 sin(4). n=0
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS