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

Printable View

- Oct 19th 2010, 07:00 AMSambitsimplification of sum and product
$\displaystyle \sum_{m=0}^{5}[\prod_{n=0, n=/=m}^{5}(\frac{x-n}{m-n})] = ?$

- Oct 19th 2010, 07:28 AMemakarov
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.

- Oct 19th 2010, 07:36 AMSambit
so what will be the

**final answer**? 1 + 1 + 1+ 1 + 1 = 5 ?

ok ok. i got it. thanks