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Math Help - Binomial problems (Urgent)

  1. #1
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    May 2008
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    Binomial problems (Urgent)

    If (1+x)n = 1+C1x+C2x2+C3x3++Cnxn
    1 ) Prove that: C0/1 - C1 /2 + C2/3 - + (-1)n Cn /(n+1) = 1/(n+1)
    2) Prove that : C0/1 + C1 /2 + C2/3 + + Cn /(n+1) = {2(n+1) - 1}/(n+1)
    3 ) Prove that : C1/ C0 + 2C2 / C1+ 3C3/ C2 ++ n .Cn / Cn -1 = n(n+1)/2
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  2. #2
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    Mar 2009
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    Grenoble
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    Most difficult task is writing the formula in LaTeX form :P

    f(x) = (1+x)^n = 1 + C_1 x + C_2 x^2 + ... + C_n x^n

    Q1 : integrate the function, so that every x^k becomes x^{k+1} / (k+1)
    Then you just replace x by some particular value.

    Q2 : similar trick

    Q3 : I don't know; keep trying stuff like "derive" / "integrate" / "replace x by ..."
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