My problem:
Let $x_0, x_1, . . . , x_n ∈ R$ be a set of pairwise distinct sample locations and let $x → L_i(x)$ be the corresponding Lagrange basis polynomials. Show that: $ \sum_{1 = 0}^{n}L_i(x) ≡ 1.$
My take: So we know the interpolating polynomial $p$ for $f=1$ equals the sum $S$ of the Lagrange polynomials. As I've understood $f$ is a polynomial with degree 0. And the interpolating polynomial is $p=f$. Further, the sum of Lagrange polynomials is 1, so $ p = S$. So my function $L_i ≡ 1$ suggest that $L_i ≡ x_n$.
Am I on right track?