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Math Help - Counting Proof...

  1. #1
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    Counting Proof...

    I am not sure where to start with this problem.

    If n is a positive integer and n > 1, prove that C(n, 2) + C(n-1, 2) is a perfect square.



    Any hints would be appreciated.
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  2. #2
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    Hello, MasterShake!

    I am not sure where to start with this problem. . . . . really?

    If n is a positive integer and n > 1,
    prove that: . C(n, 2) + C(n-1, 2) is a perfect square.

    Do you know what those C-expressions mean?
    If you do, just do the algebra . . .

    C(n,2) +C(n-1,2) \;=\;\frac{n!}{2!(n-2)!} + \frac{(n-1)!}{2!(n-3)!} \;=\;\frac{n(n-1)}{2} + \frac{(n-1)(n-2)}{2} . . . etc.

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  3. #3
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    I was aware of nCr expresion

    Even after trying to plug the equation I still am unsure how to set up the proof.

    C(n, r) = n! / r!(n-r)!

    shouldn't the bases of both equations be 2!(n-2)!
    Last edited by MasterShake; September 20th 2007 at 03:59 PM. Reason: reviewed coment output
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  4. #4
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    Quote Originally Posted by MasterShake View Post
    Even after trying to plug the equation I still am unsure how to set up the proof.

    C(n, r) = n! / r!(n-r)!

    shouldn't the bases of both equations be 2!(n-2)!
    No. In the second expression we have an n - 1 and r = 2, so (n - 1) - 2 = n - 3.

    -Dan
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