How do I show that for any x0 < x1 < x2 < ... < xn, the fundamental Lagrange polynomials satisfy
(the summation from j = 0 to n of lj(x)) = 1
where lj(x) is the jth fundamental Lagrange polynomial of degree n ?
I've been trying to work this out algebraically, but I don't really know where to start. Thanks for any help.