Something I can't seem to prove

  • Thread starter Skynt
  • Start date
  • #1
39
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:

Answers and Replies

  • #2
CRGreathouse
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Notice that [n - i] * [n - (i + 1)]! = [n - i]!.
 
  • #3
39
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obviously *bangs head* thanks!
 
  • #4
HallsofIvy
Science Advisor
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That is, by the way, the formula used for producing Pascal's triangle.
 

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