For the alternating series

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

Problem

\displaystyle \sum_{n=1}^{\infty} (-1)^{n+1}\tfrac{1}{n^{3}}

, determine the smallest integer

N

so that the difference between the exact sum of the series and the partial sum

S_N

is less than

0.0005