For the series

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

For the series ∑k=1∞(−1)k+11k3\displaystyle \sum_{k=1}^{\infty} (-1)^{k+1}\frac{1}{k^{3}}, let ENE_N denote the absolute error when the NNth partial sum SNS_N is used to approximate the full series. Student X uses S4S_4 and Student Y uses S5S_5. By approximately what factor is the guaranteed error E5E_5 smaller than the guaranteed error E4E_4? (a) About 1.01.0 times smaller (no change) (b) About 0.830.83 times smaller (c) About 0.580.58 times smaller (d) About 3.43.4 times smaller

Related theory

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