The series converges to a sum

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

Problem

The series ∑k=1∞1k3\displaystyle\sum_{k=1}^{\infty}\frac{1}{k^{3}} converges to a sum SS. Let S5=∑k=151k3S_5=\sum_{k=1}^{5}\frac{1}{k^{3}}. What is the largest value that the error ∣S−S5∣|S-S_5| can take? (a) 4.0×10−24.0\times10^{-2} (b) 2.0×10−22.0\times10^{-2} (c) 1.4×10−21.4\times10^{-2} (d) 4.6×10−34.6\times10^{-3}

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