Problem 1. (15 points) You are given that * *2k+1 sin 1 = _(-1)* ( 2k + 1)! = *- 31 + 51 - 71+ .. (a) Use the above formula to derive the Maclaurin series of cos(z?), indicating our method. Express your answer both in summation notation and by writing out the first four nonzero terms. writing out the first four nonzero terms. as a series of numbers. Express your answer both in sum ( b ) Integrate the series in ( a ) term by term to write the integral OT/T IP ( 2 ) 500 = 1 nd by with an error of