For the series

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

Problem

For the series ∑k=1∞1k3\displaystyle \sum_{k=1}^{\infty} \dfrac{1}{k^{3}}, let R20=S−S20R_{20}=S-S_{20} denote the remainder after the first 2020 terms. Which of the following values is the best upper bound for R20R_{20}? (a) 0.001130.00113 (b) 0.001250.00125 (c) 0.002500.00250 (d) 0.0001080.000108

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