$\displaystyle \sum_{m=0}^{5}[\prod_{n=0, n=/=m}^{5}(\frac{x-n}{m-n})] = ?$
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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.
so what will be the final answer? 1 + 1 + 1+ 1 + 1 = 5 ? ok ok. i got it. thanks