The series is approximated by the partial sum

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

Problem

The series S=∑n=1∞(−1) n+11n3S=\displaystyle\sum_{n=1}^{\infty}(-1)^{\,n+1}\dfrac{1}{n^{3}} is approximated by the partial sum S5S_{5}. Calculate the maximum possible absolute error when S5S_{5} is used to approximate SS, and determine whether this approximation satisfies the requirement that the error be less than 0.0020.002.

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