Lagrange Cardinal Function Proof

Question

How can I use the Lagrange interpolation polynomial $$p(x) = \sum_{i=0}^n ℓ_i(x)f(x_i)$$ that interpolates $f(x)$ at distinct points: $x_0 , x_1, ..., x_n$ where $ℓ_i(x)$’s are cardinal functions to show that $$\sum^n_{i=0}ℓ_i(x) = 1$$, for all x?

Answer 1

Use the interpolation polynomial on $f(x)=1$