Use the Definition to Find the Taylor Series Centered At c

Multiple Choice

Use the definition to find the Taylor series centered at
$c = 0 \text { for the function }$ $f ( x ) = 3 \ln \left( x ^ { 2 } + 1 \right)$

A) $3 \ln \left( x ^ { 2 } + 1 \right) = \sum _ { n = 0 } ^ { \infty } \frac { ( 3 x ) ^ { 2 n + 2 } } { n + 1 }$
B) $3 \ln \left( x ^ { 2 } + 1 \right) = 3 \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { x ^ { n + 1 } } { n + 1 }$
C) $3 \ln \left( x ^ { 2 } + 1 \right) = 3 \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } \frac { x ^ { 2 n + 2 } } { n + 1 }$
D) $3 \ln \left( x ^ { 2 } + 1 \right) = 3 \sum _ { n = 0 } ^ { \infty } \frac { x ^ { 2 n + 2 } } { n }$
E) $3 \ln \left( x ^ { 2 } + 1 \right) = \sum _ { n = 0 } ^ { \infty } \frac { ( 3 x ) ^ { n + 1 } } { n + 1 }$