To prove: That the series ∑ n = 0 ∞ ( 2 n ) ! x 2 n + 1 ( 2 n n ! ) 2 ( 2 n + 1 ) converges to arcsin x on the interval ( − 1 , 1 ) by using the power series solution of the differential equation ( 1 − x 2 ) y ″ − x y ′ = 0 .

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Answer 1

Question

Chapter 16.4, Problem 24E

To determine

To prove: That the series ∑n=0∞(2n)!x2n+1(2nn!)2(2n+1) converges to arcsinx on the interval (−1,1) by using the power series solution of the differential equation (1−x2)y″−xy′=0.

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Answer 2

Question

Chapter 16.4, Problem 24E

To determine

To prove: That the series ∑n=0∞(2n)!x2n+1(2nn!)2(2n+1) converges to arcsinx on the interval (−1,1) by using the power series solution of the differential equation (1−x2)y″−xy′=0.

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Answer 3

Question

Chapter 16.4, Problem 24E

To determine

To prove: That the series ∑n=0∞(2n)!x2n+1(2nn!)2(2n+1) converges to arcsinx on the interval (−1,1) by using the power series solution of the differential equation (1−x2)y″−xy′=0.

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Answer 4

Question

Chapter 16.4, Problem 24E

To determine

To prove: That the series ∑n=0∞(2n)!x2n+1(2nn!)2(2n+1) converges to arcsinx on the interval (−1,1) by using the power series solution of the differential equation (1−x2)y″−xy′=0.

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Answer 5

Chapter 16.4, Problem 24E

To determine

To prove: That the series ∑n=0∞(2n)!x2n+1(2nn!)2(2n+1) converges to arcsinx on the interval (−1,1) by using the power series solution of the differential equation (1−x2)y″−xy′=0.

Answer 6

Chapter 16.4, Problem 24E

To determine

To prove: That the series ∑n=0∞(2n)!x2n+1(2nn!)2(2n+1) converges to arcsinx on the interval (−1,1) by using the power series solution of the differential equation (1−x2)y″−xy′=0.

Answer 7

Chapter 16.4, Problem 24E

To determine

To prove: That the series ∑n=0∞(2n)!x2n+1(2nn!)2(2n+1) converges to arcsinx on the interval (−1,1) by using the power series solution of the differential equation (1−x2)y″−xy′=0.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 16.1 - Exactness What does it mean for the...Ch. 16.1 - Integrating Factor When is it beneficial to use an...Ch. 16.1 - Testing for Exactness In Exercises 3-6, determine...Ch. 16.1 - Testing for Exactness In Exercises 3-6, determine...Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Solving an Exact Differential Equation In...Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E

To prove: That the series ∑ n = 0 ∞ ( 2 n ) ! x 2 n + 1 ( 2 n n ! ) 2 ( 2 n + 1 ) converges to arcsin x on the interval ( − 1 , 1 ) by using the power series solution of the differential equation ( 1 − x 2 ) y ″ − x y ′ = 0 .

Solution Summary: The author proves that the series displaystyle 'underset'n=0oversetinfty'sum converges to mathrmarcsinx on

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To prove: That the series ∑n=0∞(2n)!x2n+1(2nn!)2(2n+1) converges to arcsinx on the interval (−1,1) by using the power series solution of the differential equation (1−x2)y″−xy′=0.

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Chapter 16 Solutions