Approximate the Sum of the Series by Using the First $\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } 4 } { n ! }$

Multiple Choice

Approximate the sum of the series by using the first six terms. $\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } 4 } { n ! }$

A) $1.457 < S < 1.477$
B) $1.417 < S < 1.497$
C) $1.467 < S < 1.472$
D) $1.427 < S < 1.467$
E) $1.461 < S < 1.473$