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Homework Help: Use binomial theorem to prove

  1. May 21, 2007 #1
    Use binomial theorem to prove

    C(n,0) - 3(C(n,1)) + 9(C(n,2) - 27(C(n,3) + ... + (-3)^n(C(n,n) = (-2)^n


    From looking at the data given b = (-3) so a = 1 so (-2)^n = (1-3)^n

    With this I know the equation in sigma notation and could probably prove the theorem through mathematical induction but I'm not certain that is what they are looking for in this case....

    Update:

    I proved n=1 and assumed n = k, so do I need to prove n= k+1 through mathematical induction?
     
    Last edited: May 21, 2007
  2. jcsd
  3. May 21, 2007 #2
    Doesn't writing out the expression for [tex](1+x)^n[/tex] where x=-3 constitute proof?

    edit: it's [tex](1+x)^n[/tex]
     
    Last edited: May 22, 2007
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