Use the Power Series $\frac { 1 } { 1 - x } = \sum _ { n = 0 } ^ { \infty } x ^ { n } , | x | < 1$

Multiple Choice

Use the power series $\frac { 1 } { 1 - x } = \sum _ { n = 0 } ^ { \infty } x ^ { n } , | x | < 1$
to determine a power series for the function $f ( x ) = \frac { 5 x } { ( 1 - 5 x ) ^ { 2 } }$ .

A) $\sum _ { n = 1 } ^ { \infty } n ( - 1 ) ^ { n } ( 5 x ) ^ { n + 1 }$
B) $\sum _ { n = 1 } ^ { \infty } n ( - 1 ) ^ { n } ( 5 x ) ^ { n }$
C) $\sum _ { n = 1 } ^ { \infty } n ( 5 x ) ^ { n }$
D) $\sum _ { n = 1 } ^ { \infty } n ( 5 x ) ^ { n - 1 }$
E) $\sum _ { n = 1 } ^ { \infty } n ( 5 x ) ^ { n + 1 }$