Let ∑k=1[infinity](−1)k+1ak be a convergent alternating series with terms that are nonincreasing in magnitude. Let Rn=S−Sn be the remainder in approximating the value of that series by the sum of its first n terms. Then Rn≤an+1. In other words, the magnitude of the remainder is less than or equal to the magnitude of the first neglected term. For the convergent alternating series ∑k=0[infinity] (−1)k (2k+1)4, evaluate the nth partial sum for n=2. Then find an upper bound for the error S−Sn in using the nth partial sum Sn to estimate the value of the series S.