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?

I'm not entirely sure why they choose to write it that way.
$$G(x) = \frac{1}{1-x} = \sum\limits_{n=0}^\infty x^n$$
$$G'(x) = \frac{1}{(1-x)^2} = \sum\limits_{n=0}^\infty nx^{n-1} = \sum_{n=0}^{\infty } \binom{n+1}{n}x^n$$
This is a minor reindexing, after noting that
$$\binom{n+1}{n} = \binom{n+1}{1} = n+1$$
It appears have been written in a deliberately obtuse manner, though perhaps it facilitates the application of Pascal's identity or similar later on?
