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Math Help - verify uh...

  1. #1
    Member billym's Avatar
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    verify uh...

    Greetings math gods. This class is killing me. I don't mind when questions involve numbers but I hate stuff like this.


    Verify: \frac{n!} { 2!(n-2)!} = \frac{k!}{ 2!(k-2)!} + k(n-k) +\frac{ (n-k)!}{2!(n-k-2)!}<br />

    Note: the original question was use the factorial definition of C(m,r) to verify that:

    C(n,2) = C(k,2) + k(n-k) + C(n-k,2) 1 <= k <= n


    I really have no idea where to begin. How do you manipulate this ?
    Last edited by mr fantastic; September 30th 2009 at 10:33 PM. Reason: Clarified the question in light of later posts.
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  2. #2
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    Quote Originally Posted by billym View Post
    Greetings math gods. This class is killing me. I don't mind when questions involve numbers but I hate stuff like this.


    Verify: \frac{n!} { 2!(n-2)!} = \frac{k!}{ 2!(k-2)!} + k(n-k) +\frac{ (n-k)!}{2!(n-k-2)!}<br />

    Note: the original question was use the factorial definition of C(m,r) to verify that:

    C(n,2) = C(k,2) + k(n-k) + C(n-k,2) 1 <= k <= n


    I really have no idea where to begin. How do you manipulate this ?
    LHS = \frac{n(n-1)}{2}.

    RHS = \frac{k(k-1)}{2} + k(n-k) + \frac{(n-k)(n-k-1)}{2}.

    Your job is to further simply the RHS and hence show that it's equal to the LHS.
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