For an alternating series whose summands are decreasing in magnitude, the true sum S lies between any two successive partial sums: (*) min {SN, SN+1} <≤ S≤ max {SN, SN+1}. Consider S=> TUNC1 (-1)+1 1 n5 and write Answer: S (a) Find the smallest value of N for which the interval bracketing S in line (*) above has length at most 10-⁹. SN=(-1)+1 n5 n=1 Answer: Nmin == (b) Using the N found in part (a), approximate S by the midpoint of the interval implicit in line (*). A spreadsheet may be helpful to calculate the sum SN. SN + SN+1 2

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