Use the Definition to Find the Taylor Series Centered At c

Multiple Choice

Use the definition to find the Taylor series centered at $c = 0 \text { for the function }$ $f ( x ) = \sin 4 x$

A) $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } ( 4 x ) ^ { 2 n - 1 } } { ( 2 n - 1 ) ! }$
B) $\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { n } ( 4 x ) ^ { 2 n + 1 } } { ( 2 n + 1 ) ! }$
C) $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n + 1 } ( 4 x ) ^ { 2 n + 1 } } { ( 2 n + 1 ) ! }$
D) $\sum _ { n = 0 } ^ { \infty } \frac { ( - 1 ) ^ { 2 n - 1 } ( 4 x ) ^ { 2 n - 1 } } { n ! }$
E) $\sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } ( 4 x ) ^ { 2 n + 1 } } { ( 2 n + 1 ) ! }$