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Math Help - Proof of a series with binomial coefficients

  1. #1
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    Proof of a series with binomial coefficients

    I don't have any experience dealing with binomial coefficients, so I'm really confused on how to do this following problem. I wrote the binomial coefficients in parenthesis with some space between where the top and bottom part should be (not sure how to format it otherwise

    Problem: Prove that

    n
    Sigma (n i) = 2^n
    i=0

    and

    n
    Sigma (-1)^n * (n i) = 0
    i=0


    I'm not sure if I need to use induction or not to prove either of these and I'm not sure where I'd start even the base of induction if I did have to.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by uberbandgeek6 View Post
    I don't have any experience dealing with binomial coefficients, so I'm really confused on how to do this following problem. I wrote the binomial coefficients in parenthesis with some space between where the top and bottom part should be (not sure how to format it otherwise

    Problem: Prove that

    n
    Sigma (n i) = 2^n
    i=0

    and

    n
    Sigma (-1)^n * (n i) = 0
    i=0


    I'm not sure if I need to use induction or not to prove either of these and I'm not sure where I'd start even the base of induction if I did have to.
    The first can be done in a plethora of ways. I guess the easiest is to note that both are forms of the binomial expansion.
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