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Binomial Theorem-related proof?

  • 28-04-2011 6:29pm
    #1
    RHRN
    Closed Accounts Posts: 357 ✭✭


    Hi, wondering if anyone can help me.

    Working from Burton's Number Theory, and looking to prove that:

    ( sorry for the shoddy notation, don't know how to do it otherwise, so I'll use xCy as x choose y)

    nCk = (n-2)C(k-2) + 2((n-2)C(k-1)) + (n-2)Ck

    So I took my right hand side, wrote everything in the form

    x!/y!(x-y)! and simplified the right side, but ended up with:

    (n-2)!(n+2)(n+1)/k!(n-(k-2))!

    So I'm definitely wrong... but I don't know how to progress, or if I've gone wrong earlier?

    I wrote the whole thing as a fraction with k!(n-(k-2))! as the common denominator... But I wasn't sure doing it, and I don't really know how to proceed (or start again).

    Help would be greatly appreciated, thanks :)


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