Approximate the Sum to the Indicated Accuracy $\sum _ { n = 1 } ^ { \infty } \frac { 4 ( - 1 ) ^ { n - 1 } } { n ^ { 7 } }$

Multiple Choice

Approximate the sum to the indicated accuracy.
$\sum _ { n = 1 } ^ { \infty } \frac { 4 ( - 1 ) ^ { n - 1 } } { n ^ { 7 } }$ (five decimal places)

A) $6.97036$
B) $4.97036$
C) $7.97036$
D) $3.97036$
E) $5.97036$