Approximating the sum of an alternating series. If the alternating series (-1)"+'b satisfies the requirements for the alternating series test, 1. b, > 0 for all n 2. b, > bn+1 for all n > N where N is an integer 3. b, → 0 as n 0 Then, for n > N, S, = E(-1)k++bx = bị – b2 + b3 – b4+...+(-1)"+b, k1 approximates the sum of the series, S, such that |S – S„| < bn+1. In other words, the size of the approximation error is smaller than the n + 1st term, bn+1 How many terms of the series do we need to add in order to find the sum to the indicated accuracy? (-1)"+1 error < 0.005 terms are needed. WI

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