# Thread: simplification of sum and product

1. ## simplification of sum and product

$\sum_{m=0}^{5}[\prod_{n=0, n=/=m}^{5}(\frac{x-n}{m-n})] = ?$

2. This is a Lagrange polynomial of degree 5 that is equal to 1 at x = 0, 1, 2, 3, 4, 5. There is only one such polynomial, namely y(x) = 1.

3. so what will be the final answer? 1 + 1 + 1+ 1 + 1 = 5 ?

ok ok. i got it. thanks