Find a power series representation for $f(x)=\frac{1}{(1+x{)}^2}$

${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^{n+1}{x}^{2n-2}$

${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^{n+1}{x}^{n-1}$

${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^{n+1}n{x}^{n-1}$

${\displaystyle \underset{n=1}{\overset{}{}}}n{x}^{n-1}$

${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^{n+1}n!x^{n-1}$