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2. The series = 6 (2n)! 24n +1 (n!)? (2n + 1) n = 0 3 1.3 2.4.5 1.3 5 2.3 2, + 2.4.6.72) + • has been attributed to Newton in the late 1600s. The proof of this result uses the Maclaurin series for f(x) = sin-x. a. Prove that the series converges. b. Evaluate the partial sums Sn for n = 5, 10, 20. C. Compare Sn to t for n = 5, 10, 20 and discuss the number of correct decimal places.

2. The series = 6 (2n)! 24n +1 (n!)? (2n + 1) n = 0 3 1.3 2.4.5 1.3 5 2.3 2, + 2.4.6.72) + • has been attributed to Newton in the late 1600s. The proof of this result uses the Maclaurin series for f(x) = sin-x. a. Prove that the series converges. b. Evaluate the partial sums Sn for n = 5, 10, 20. C. Compare Sn to t for n = 5, 10, 20 and discuss the number of correct decimal places.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. The series (2n)! %3D n = 0 2 +' (n!)² (2n + 1) 1. 2.3 1.3 2.4.5 2 5 _1.3.5 2.4.6 7 2 has been attributed to Newton in the late 1600s. The proof of this result uses the Maclaurin series for f(x) = sin-x. %3D a. Prove that the series converges. b. Evaluate the partial sums Sn for n = 5, 10, 20. C. Compare Sn to t for n= 5, 10, 20 and discuss the number of correct decimal places.
Transcribed Image Text:2. The series (2n)! %3D n = 0 2 +' (n!)² (2n + 1) 1. 2.3 1.3 2.4.5 2 5 _1.3.5 2.4.6 7 2 has been attributed to Newton in the late 1600s. The proof of this result uses the Maclaurin series for f(x) = sin-x. %3D a. Prove that the series converges. b. Evaluate the partial sums Sn for n = 5, 10, 20. C. Compare Sn to t for n= 5, 10, 20 and discuss the number of correct decimal places.
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