Let be the sum of the convergent series

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

Problem

Let SS be the sum of the convergent series ∑k=1∞1k2\displaystyle\sum_{k=1}^{\infty}\frac{1}{k^{2}}. Determine the least integer NN such that the partial sum SNS_N guarantees ∣S−SN∣<0.001|S-S_N|<0.001. (a) N=1000N=1000 (b) N=32N=32 (c) N=1001N=1001 (d) N=999N=999

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