This is what I have to prove:
$$f[x_0, x_1, \dots, x_n] = \frac{(-1)^n}{(x_0+a)(x_1+a) \dots (x_n+a)}$$
where $f(x) = \frac{1}{x+a}$ and $f[x_0, \dots, x_n]$ is the divided difference of $f$ in these points. I know that in the proof is used this
Lemma : $(fg)[x_0, \dots,x_n] = \sum_{k = 0}^{n}f[x_0,\dots,x_k]g[x_k,\dots,x_n]$
Don't know how though...
