Approximate the Sum of the Series by Using the First $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } 2 } { n ^ { 3 } }$

Multiple Choice

Approximate the sum of the series by using the first six terms. $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } 2 } { n ^ { 3 } }$

A) $1.799 < S < 1.805$
B) $1.794 < S < 1.806$
C) $1.794 < S < 1.805$
D) $1.792 < S < 1.792$
E) $1.698 < S < 1.902$