Let $f(x)=x^n$ for $n \in \mathbb{N}$. Prove that $f[x_0,x_1,\ldots,x_n]=1$, where $\{x_i\}$ are distinct $n+1$ real numbers.
I tried doing this by finding an interpolation of the function and by using Newton's form but what I did didn't lead to the solution.
I also tried using the definition as given in Wikipidia but that didn't help me either. Any ideas on how to prove this ?
[This question is taken from the book Numerical analysis by David Ronald Kincaid, Elliott Ward Cheney]