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Math Help - Binomial Thm

  1. #1
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    Binomial Thm

    Use the binomial theorem to Prove:

    The sum as k=0 --> n OF (nCk)*2^k = 3^n

    Thanks...
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  2. #2
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    So you want to prove that

    \displaystyle\sum_{k=0}^{n}{n\choose k} 2^{k}=3^{n}, right?

    Have you had any ideas so far?
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  3. #3
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    Yes thats correct. And no, I don't see what to do...
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  4. #4
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    Quote Originally Posted by jzellt View Post
    And no, I don't see what to do...
    Hint: 1 to any power is 1, i.e. 1 = (1)^{n-k}.
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  5. #5
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    I just really don't see this one. Is it possible for someone to show me the proof? Thanks
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  6. #6
    Senior Member BAdhi's Avatar
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    (a+b)^n=\displaytype{\sum_{k=0}^n \binom{n}{k}b^ka^{n-k}}

    consider a=1 and b=2
    Last edited by BAdhi; March 2nd 2011 at 08:56 PM. Reason: latex error
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  7. #7
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    I think I can go from here... Thanks!
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