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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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