MHB How to Prove the Lagrange Interpolation Formula?

[HMPARTICLE]

$\text{Let } L_{n,i}, i = 0,...,n, \text{be the Lagrange nodal basis at} x_0 < x_1<...<x_n$. Show that, for any polynomial $q \in P_n$

$$\sum_{i=0}^nq(x_i)L_{n,i}(x)= q(x)$$

I don't know how to begin this proof. I know what a lagrange polynomial is, but I am not sure how to begin. If someone could give me a point to start please.

 

[Nikolas7]

Are you need to prove interpolation formula of Lagrange?