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Math Help - Proof using Binomial Theorem

  1. #1
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    Proof using Binomial Theorem

    Hey all,

    I am stuck on trying to prove 2^n = \sum_{r=0}^r \begin{pmatrix} n\\ r \end{pmatrix} using the Binomial Theorem, any ideas ? Thanks
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    Quote Originally Posted by Oiler View Post
    Hey all,

    I am stuck on trying to prove 2^n = \sum_{r=0}^r \begin{pmatrix} n\\ r \end{pmatrix} using the Binomial Theorem, any ideas ? Thanks
    Hint:

    2=1+1 (In most of the times)
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  3. #3
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    Quote Originally Posted by Oiler View Post
    2^n = \sum_{r=0}^r \begin{pmatrix} n\\ r \end{pmatrix} using the Binomial Theorem
    This is a standard theorem if we know that \left( {a + b} \right)^n  = \sum\limits_{k = 0}^n {\binom{n}{k}a^k b^{n - k} }
    Now let a=1~\&~b=1

    NOTE you have a mistake. The upper limit in n.
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