The Maclaurin series representation of $f ( x ) = \frac { 1 } { ( 1 + x ) ^ { 2 } }$ is

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

Question

The Maclaurin series representation of $f ( x ) = \frac { 1 } { ( 1 + x ) ^ { 2 } }$ is

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

Quizplus · Accepted Answer

The Answer of The Maclaurin series representation of $f ( x ) = \frac { 1 } { ( 1 + x ) ^ { 2 } }$ is

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

The Maclaurin Series Representation Of f(x)=1(1+x)2f ( x ) = \frac { 1 } { ( 1 + x ) ^ { 2 } }f(x)=(1+x)21​

The Maclaurin Series Representation Of $f ( x ) = \frac { 1 } { ( 1 + x ) ^ { 2 } }$