2. The series _ on (2n)! 2: _ 6 2n=0 24"+1(n!)2(2n+l) 3 , 5 .. 7 =6(%+2+3(%) +-G) music) +---) has been attributed to Newton in the late 16003. The proof of this result uses the Maclaurin series for f (x) = sin1x. a. Prove that the series converges. b. Evaluate the partial sums S" for n = 5, 10, 20. c. Compare S, to it for n = 5, 10, 20 and discuss the number of correct decimal places.