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Something I can't seem to prove

  1. Jun 29, 2009 #1
    It should be really simple, but I think the algebra is bogging me down:

    [tex]\frac{n!}{(n-i)! i!} + \frac{n!}{[n-(i+1)]! (i+1)!} = \frac{(n+1)!}{(n-i)! (i+1)!}[/tex]

    Can anyone show me the process of proving this? I don't see how the two expressions are equal...

    essentially I can't get rid of the [n - (i + 1)]! term when I try to combine the two fractions and expand things.
     
    Last edited: Jun 29, 2009
  2. jcsd
  3. Jun 30, 2009 #2

    CRGreathouse

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    Notice that [n - i] * [n - (i + 1)]! = [n - i]!.
     
  4. Jun 30, 2009 #3
    obviously *bangs head* thanks!
     
  5. Jun 30, 2009 #4

    HallsofIvy

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    That is, by the way, the formula used for producing Pascal's triangle.
     
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