I did the same problem about 6 months ago. If I remember well, you have to use the definition of Lagrange polynomial : check out Lagrange polynomial - Wikipedia, the free encyclopedia.

I have no time to help you more (so sorry about that), but in, don't you mean the product instead of the summation?(the summation from j = 0 to n of lj(x)) = 1

where lj(x) is the jth fundamental Lagrange polynomial of degree n ?