How am I supposed to know that $\frac{1}{(1-x)^2} = \sum_{n=0}^{\infty } \binom{n+1}{n}x^n$? I'm currently reading through the solution to a problem that involves finding generating functions. In some of the intermediary steps, it is written that
$$\frac{1}{(1-x)^2} = \sum_{n=0}^{\infty } \binom{n+1}{n}x^n$$
without any justification.
Is there some kind of reasoning behind this or is this just one of those things I have to accept?

Keep in mind that in general for $\alpha\in \mathbb{R}$ you have $$(1+x)^\alpha = \sum_{n=0}^{\infty} {\alpha \choose n}x^n$$ by Taylor series.  
