1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted