Approximating the sum of an alternating series. If the alternating series Ž(-1)"b, satisfies the requirements for the alternating series test 1. by > 0 for all n 2. b, bu+1 for all n N where N is an integer 3. b. - O as n00 Then, for η ΣN, 1 S = (-1)*b* = -b+ b2 - b3 + bx + ... + (-1)" bn k1 approximates the sum of the series, S, such that IS-SIS bath. In other words, the size of the approximation error is smaller than the n+ 1 st term, bu+1 Ë (-1) Given the series determine the number of terms n! needed to approximate the sum of the series correct to three decimal places. Then, find the sum of the series correct to three decimal places. terms are needed to write the sum of the series correct to three decimal places. The sum of the series, correct to three decimal places is