Representing Functions as Power Series Rewrite $$f(x)=(1+x)/(1-x)^2$$ as a power series.
Work thus far:
I separated it into two parts:
$$1/(1-x)^2 + x/(1-x)^2$$
I realize that the first expression is the derivative of $1/(1-x)$ and come up with this sum of series:
$$\sum_{n=0}^\infty x^n$$
Since a derivative was involved, we must derive the series:
$$\displaystyle\sum_{n=0}^\infty nx^{n-1} + x \displaystyle\sum_{n=0}^\infty nx^{n-1}$$
$$=\displaystyle\sum_{n=0}^\infty nx^{n-1} + \displaystyle\sum_{n=0}^\infty nx^n$$
These series need to be added, but how? 
The final answer is $\displaystyle\sum_{n=0}^\infty (2n+1)x^n$

$$
\frac{1}{1-x}=1+x+x^2+x^3+\ldots
$$
$$
\frac{1}{(1-x)^2}=1+2x+3x^2+4x^3+\ldots
$$
$$
\frac{1+x}{(1-x)^2}=1+2x+3x^2+\ldots +x+2x^2+ 3x^3+\ldots=1+3x+5x^2+7x^3+\ldots
$$
