Use the Definition to Find the Taylor Series (Centered at C)

Multiple Choice

Use the definition to find the Taylor series (centered at c) for the function. $$f ( x ) = e ^ { 2 x } , c = 0$$

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