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Deriving identity - need help

  1. Sep 14, 2008 #1
    deriving identity - need help!!!

    1. The problem statement, all variables and given/known data

    Derive for S[tex]^{p}_{n}[/tex] = 1[tex]^{p}[/tex] + ... + n[tex]^{p}[/tex] the identity

    (p+1)*S[tex]^{p}_{n}[/tex] + (p+1 choose 2)*S[tex]^{p-1}_{n}[/tex] + ...+S[tex]^{0}_{n}[/tex] = (n+1)*[tex]^{p+1}[/tex] - 1

    2. Relevant equations

    Um, I know that the S[tex]^{1}_{n}[/tex] = n(n+1)/2
    S[tex]^{2}_{n}[/tex] = n(n+1)(2n+1)/6
    S[tex]^{3}_{n}[/tex] = [1+2+...+n]^2

    3. The attempt at a solution

    I have NO idea how to show this. I tried writing out some of the terms, but I didn't really get anywhere. I am completely lost as to how my lhs is supposed to become (n+1)^ anything... yeah... all I know is that I can write out the p choose n kind of terms, but so far that hasn't really yielded anything useful. Please help! I am so confused!! :cry:
     
  2. jcsd
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