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Thread: simplification of sum and product

  1. October 19th 2010, 07:00 AM #1
    Sambit
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    Question simplification of sum and product

    \sum_{m=0}^{5}[\prod_{n=0, n=/=m}^{5}(\frac{x-n}{m-n})] = ?
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  2. October 19th 2010, 07:28 AM #2
    emakarov
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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.
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  3. October 19th 2010, 07:36 AM #3
    Sambit
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    so what will be the final answer? 1 + 1 + 1+ 1 + 1 = 5 ?

    ok ok. i got it. thanks
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