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Math Help - help with binomal question

  1. #1
    Junior Member
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    help with binomal question

    I dont know how to do the signals so ill right in words everything....


    (1-1)^n = n SIGMA k=0 nCk * 1^k *(-1)^(n-k)

    why does it equals to:
    n SIGMA k=0 nCk * (-1)^k



    i dont understand why (-1)^(n-k) become (-1)^k



    someone can help me please???
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  2. #2
    MHF Contributor

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    The following expansion can be written in two ways.
    Note the placement of the exponents in the equivalent sums.
    \left( {a + b} \right)^n  = \sum\limits_{k = 0}^n {{n \choose k}\left( a \right)^k \left( b \right)^{n - k} } \;\text{OR} \,\sum\limits_{k = 0}^n {{n \choose k}\left( a \right)^{n - k} \left( b \right)^k }
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