For the series

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

Problem

For the series

\displaystyle \sum_{k=1}^{\infty}(-1)^{k+1}\frac{1}{k^{3}}

, determine the least integer

N

such that the remainder after

N

terms has magnitude less than

10^{-4}

. (a)

26

(b)

21

(c)

22

(d)

20