Answer
$x^2-x^3+x^4-x^5+...+(-x^{n+2})...$
for $r$ in $(-1,1)$
Work Step by Step
We are given $f(x)=\frac{x^2}{x+1}=\frac{x^2}{1-(-x)}$
for $r$ in $(-1,1)$
The Taylor series for $\frac{1}{1-x}$ is
$1+x+x^2+x^3+...+x^n+...$
The Taylor series for $f(x)=\frac{x^2}{1-(-x)}$ is
$f(x)=x^2.1+x^2(-x)+x^2(-x)^2+x^2(-x)^3...+x^2(-x)^n+...$
$=x^2-x^3+x^4-x^5+...+(-x^{n+2})...$
