Determine the Minimal Number of Terms Required to Approximate the Sum

Multiple Choice

Determine the minimal number of terms required to approximate the sum of the series with an error of less than 0.007.
$\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } } { n ^ { 3 } }$

A) 5
B) 4
C) 2
D) 6
E) 3