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Math Help - Binomial Coefficient Problem.

  1. #1
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    Binomial Coefficient Problem.

    Q: Let n,k be a positive integer, Prove that
    1(C(n,1))+ 2(C(n,2)) +......+ n(C(n,n)) = n2^(n-1)



    Induction doesn't seem to work.. I have no idea what to do for this question.
    Please Help.

    P.S. its 2^(n-1)- dunno why it showed up like that.

    Thanks,
    Creative
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  2. #2
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    Quote Originally Posted by Creative View Post
    Q: Let n,k be a positive integer, Prove that
    1(C(n,1))+ 2(C(n,2)) +......+ n(C(n,n)) = n2^{n-1}
    Differentiate both sides of the equation (1+x)^n = C(n,0) + (C(n,1))x + (C(n,2))x^2 +\ldots+ (C(n,n))x^n. Then put x=1.

    Quote Originally Posted by Creative View Post
    P.S. its 2^(n-1)- dunno why it showed up like that.
    You need to use braces instead of parentheses: 2^{n-1}.
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  3. #3
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    So use Induction after changing it to that form?
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  4. #4
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    Quote Originally Posted by Creative View Post
    So use Induction after changing it to that form?
    You shouldn't need to use induction at all. I'm sure you are allowed to quote the binomial expansion of (1+x)^n, which is all that is needed here.
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