For the Function $g ( x ) = \frac { 1 } { 11 x ^ { 2 } + 1 }$

Multiple Choice

$\text { Use the power series } \frac { 1 } { 1 + x } = \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } x ^ { n } \text { to determine a power series centered at } 0$ for the function $g ( x ) = \frac { 1 } { 11 x ^ { 2 } + 1 }$ .

A) $\sum _ { n = 0 } ^ { \infty } ( - 11 ) ^ { n } x ^ { n }$
B) $\sum _ { n = 0 } ^ { \infty } ( 11 ) ^ { n } x ^ { 2 n }$
C) $\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } x ^ { 2 n }$
D) $\sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n } x ^ { n }$
E) $\sum _ { n = 0 } ^ { \infty } ( - 11 ) ^ { n } x ^ { 2 n }$