Let x_0,...,x_n be distinct real numbers and l_k(x) be the Lagrange's basis function. δ_n = ∏^n _{k=0}(x-x_k). Prove that a.) ∑^n_{k=0}l_k(x) ≡ 1. b.) ∑^n_{k=0}x^j_k(l_k)(x) ≡ x^j. for j = 0,1,...,n I do not know how to prove these?
