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September 3rd, 2016, 08:14 AM   #1
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pascal's triangle proof with binomial coefficients

Hey I wasn't sure exactly where to put this, but since here in the states you normally start to use binomial coefficients in stats I put it here.

So I was doing a problem in a book were I had to prove that
(n + 1 choose k) equals (n choose k - 1) + (n choose k).

I came up with the answer (which I think is probably wrong):

(n + 1) - k = n - (k - 1) + (n - k) = n - (k - 1) + (n - (n - k)) = n - (k - (k - 1)) + (n - (n - k)) = n+1-k

So I looked up a solution and found this:
Prove the law of Pascal's triangle - Stumbling Robot

Although I can't figure out how he got from the first part to the second part.. where he use the common denominator. Could someone work that part out step by step?
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September 3rd, 2016, 08:35 AM   #2
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Never mind I got it. I feel silly now lol After I finally remembered that m!(m+1) = (m+1)! The whole thing immediately was clear.

Last edited by GumDrop; September 3rd, 2016 at 08:42 AM.
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