1. Find power series representations for the following functions. State the radius of convergence. (You do NOT need to find the interval of convergence.) Make sure to write your answer in the proper form: (z-a)*, where a is the center. k=0 (a) f(x) = re centered at a = <=0 24+1 EI f(() = 2 + (x)² k=6 ROC=0 laflo Test k+1(k) | | kfl So 20C = 80 e = 2. 2 ex= T = 11 kok! R=0 k! X 26+1 kio ki 2k+1 CD (x²³² 4-0 (b) re lion Iim X O da centered at a = 0 (Use your answer to part (a)!) 4821 Kai S

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
icon
Related questions
Question
How would I find this power series and use it to solve for part b?
Show all your work. In particular, you should clearly communicate youur solution by providing arguments and
statements that are complete, logically ordered, and use proper terminology and notation.
1. Find power series representations for the following functions. State the radius of convergence. (You do NOT
need to find the interval of convergence.) Make sure to write your answer in the proper form: C (x- a)*,
where a is the center.
(a) f(x) = re
centered at a =0
2に-
o k!
ご:全)
ko k!
ROC 0
ルニロ
lasio Test
liem
こ
kio ks.
とA(
zkrl
lim
ニ
So 2OC =
(b) / ze
Flx)= į ! (x)
da centered at a = 0 (Use your answer to part (a)!)
Lい
ko k!.
%3D
1
Transcribed Image Text:Show all your work. In particular, you should clearly communicate youur solution by providing arguments and statements that are complete, logically ordered, and use proper terminology and notation. 1. Find power series representations for the following functions. State the radius of convergence. (You do NOT need to find the interval of convergence.) Make sure to write your answer in the proper form: C (x- a)*, where a is the center. (a) f(x) = re centered at a =0 2に- o k! ご:全) ko k! ROC 0 ルニロ lasio Test liem こ kio ks. とA( zkrl lim ニ So 2OC = (b) / ze Flx)= į ! (x) da centered at a = 0 (Use your answer to part (a)!) Lい ko k!. %3D 1
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax