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Math Help - Help needed for induction proof

  1. #1
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    Help needed for induction proof

    Hi

    I am trying to prove that

    \sum_{k=0}^n (-1)^k \binom{n}{k}=0 \,\, \forall n \in  N

    This has to be proved using induction. For n=1, this is certainly true. Now assume
    that its true for some m\in N. Then we have


    \sum_{k=0}^m (-1)^k \binom{m}{k}=0

    Now consider P(m+1).

    \sum_{k=0}^{m+1} (-1)^k \binom{m+1}{k}

    =\sum_{k=0}^{m} (-1)^k \binom{m+1}{k}+(-1)^{m+1}\binom{m+1}{m+1}

    =(-1)^{m+1}+\sum_{k=0}^{m} (-1)^k \binom{m+1}{k}

    Now I am trying to see where to go from here.

    Can anybody help me here ?

    newton
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  2. #2
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  3. #3
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    Priviet Makarov

    Thanks a ton. worked wonders........
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