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Math Help - sum of combinations

  1. #1
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    sum of combinations

    Hello ,
    I need help to prove that :
    (2n)! / (n! * n!) + (2n-1)! / ( (n-1)! * n! ) + (2n-2)! / ( (n-2)! * n! ) + ... + n!/( 0! * n!) = (2n+1)! / ( n! * (n+1)! )

    or C2nn + C2n-1n + ... + Cnn =C2n+1n+1

    I applied mathematical induction and it didn't work or i did something wrong.
    I appreciate your help !
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  2. #2
    MHF Contributor
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    Re: sum of combinations

    You need to generalize the statement you are proving. Show C_m^n+C_{m-1}^n+\dots+C_n^n = C_{m+1}^{n+1} by induction on m.
    Thanks from MarkFL and gambix
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  3. #3
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    Re: sum of combinations

    Thank you emakarov , i successfully applied mathematical induction on m .
    You really saved me . Thanks.
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