Apply Taylor's Theorem to Find the Power Series Centered At c

Multiple Choice

Apply Taylor's Theorem to find the power series centered at $c = 0$ for the function $f ( x ) = e ^ { 12 x }$ .

A) $\sum _ { n = 0 } ^ { \infty } \frac { ( 12 x ) ^ { n + 1 } } { ( n + 1 ) ! }$
B) $\sum _ { n = 0 } ^ { \infty } \frac { ( 12 x ) ^ { n } } { ( n + 1 ) ! }$
C) $\sum _ { n = 0 } ^ { \infty } \frac { ( 12 x ) ^ { n } } { n ! }$
D) $\sum _ { n = 1 } ^ { \infty } \frac { ( 12 x ) ^ { n + 1 } } { n ! }$
E) $\sum _ { n = 0 } ^ { \infty } \frac { ( 12 x ) ^ { n + 1 } } { n ! }$