Consider the series

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Consider the series S=∑k=1∞(−1)k1k3\displaystyle S=\sum_{k=1}^{\infty} (-1)^{k}\frac{1}{k^{3}}. Using the partial sum S4S_{4}, give a numerical upper bound for ∣S−S4∣|S-S_{4}|.

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