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Find the radius of convergence, R, of the series. (x+5)" 5 In(n) n = 2 R = 5 Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) 1 = (-10,0) × (a) Use differentiation to find a power series representation for 1 f(x) (5 + x)2 f(x) = n = 0 ΣΟ 1\n- n- 1 nx What is the radius of convergence, R? R = 5 (b) Use part (a) to find a power series for f(x) = 1 (5 + x)* 00 f(x) n = 0 (-1)" (1 n- - 5 ¹n ( n − 1 ) x" − 2 What is the radius of convergence, R? R = 5 (c) Use part (b) to find a power series for f(x): = x² (5 + x)³ f(x) = 00 Σ n = 2 (-1)" n - - 5 ) What is the radius of convergence, R? R = 5 Enhanced Feedback Please try again, keeping in mind that you can differentiate both sides of the power series expansion to obtain power series representation for the derivative of the given function. So, to find the power series representation of a function of the form a (b+cx)2' you may first find the power series representation of the function a. The resulting power series converges on the same interval. b+cx

Find the radius of convergence, R, of the series. (x+5)" 5 In(n) n = 2 R = 5 Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) 1 = (-10,0) × (a) Use differentiation to find a power series representation for 1 f(x) (5 + x)2 f(x) = n = 0 ΣΟ 1\n- n- 1 nx What is the radius of convergence, R? R = 5 (b) Use part (a) to find a power series for f(x) = 1 (5 + x)* 00 f(x) n = 0 (-1)" (1 n- - 5 ¹n ( n − 1 ) x" − 2 What is the radius of convergence, R? R = 5 (c) Use part (b) to find a power series for f(x): = x² (5 + x)³ f(x) = 00 Σ n = 2 (-1)" n - - 5 ) What is the radius of convergence, R? R = 5 Enhanced Feedback Please try again, keeping in mind that you can differentiate both sides of the power series expansion to obtain power series representation for the derivative of the given function. So, to find the power series representation of a function of the form a (b+cx)2' you may first find the power series representation of the function a. The resulting power series converges on the same interval. b+cx

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 49E
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Please help me with these questions. I am having trouble understanding what to do. I keep getting the wrong answer indicated by the Red X. Thank you

Find the radius of convergence, R, of the series. (x+5)" 5 In(n) n = 2 R = 5 Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) 1 = (-10,0) ×
Transcribed Image Text:Find the radius of convergence, R, of the series. (x+5)" 5 In(n) n = 2 R = 5 Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) 1 = (-10,0) ×
(a) Use differentiation to find a power series representation for 1 f(x) (5 + x)2 f(x) = n = 0 ΣΟ 1\n- n- 1 nx What is the radius of convergence, R? R = 5 (b) Use part (a) to find a power series for f(x) = 1 (5 + x)* 00 f(x) n = 0 (-1)" (1 n- - 5 ¹n ( n − 1 ) x" − 2 What is the radius of convergence, R? R = 5 (c) Use part (b) to find a power series for f(x): = x² (5 + x)³ f(x) = 00 Σ n = 2 (-1)" n - - 5 ) What is the radius of convergence, R? R = 5 Enhanced Feedback Please try again, keeping in mind that you can differentiate both sides of the power series expansion to obtain power series representation for the derivative of the given function. So, to find the power series representation of a function of the form a (b+cx)2' you may first find the power series representation of the function a. The resulting power series converges on the same interval. b+cx
Transcribed Image Text:(a) Use differentiation to find a power series representation for 1 f(x) (5 + x)2 f(x) = n = 0 ΣΟ 1\n- n- 1 nx What is the radius of convergence, R? R = 5 (b) Use part (a) to find a power series for f(x) = 1 (5 + x)* 00 f(x) n = 0 (-1)" (1 n- - 5 ¹n ( n − 1 ) x" − 2 What is the radius of convergence, R? R = 5 (c) Use part (b) to find a power series for f(x): = x² (5 + x)³ f(x) = 00 Σ n = 2 (-1)" n - - 5 ) What is the radius of convergence, R? R = 5 Enhanced Feedback Please try again, keeping in mind that you can differentiate both sides of the power series expansion to obtain power series representation for the derivative of the given function. So, to find the power series representation of a function of the form a (b+cx)2' you may first find the power series representation of the function a. The resulting power series converges on the same interval. b+cx
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