Determine the least integer such that the partial sum approximates the entire series…

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

Problem

Determine the least integer NN such that the partial sum SN=∑n=1N(−1)n+1nS_{N}=\displaystyle\sum_{n=1}^{N}\frac{(-1)^{n+1}}{n} approximates the entire series to within 0.0010.001. (a) N=1000N=1000 (b) N=999N=999 (c) N=500N=500 (d) N=998N=998

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