The series converges

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

Problem

The series ∑n=1∞(−1)n+11n3\displaystyle\sum_{n=1}^{\infty}(-1)^{n+1}\dfrac{1}{n^{3}} converges. Determine the least positive integer NN such that the partial sum SNS_N approximates the infinite series to within 0.00050.0005.

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