Approximate the Sum to the Indicated Accuracy $\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { 4 ^ { n } n ! }$

Approximate the sum to the indicated accuracy. $\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } } { 4 ^ { n } n ! }$