discrete mathematics - Prove Fibonacci Identity using generating functions

I have the following summation identity for the Fibonacci sequence.

$$\sum_{i=0}^{n}F_i=F_{n+2}-1$$

I have already proven the relation by induction, but I also need to prove it using generating functions, but I'm not entirely sure how to approach it.

I do know that the generating function for the fibonacci sequence is

$$F(x) = \dfrac{1}{1-x-x^2}$$

But, I'm not entirely sure if that applies here. Any help would be appreciated!