My Math Forum pascal's triangle proof with binomial coefficients

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 September 3rd, 2016, 08:14 AM #1 Member   Joined: Jan 2016 From: United States Posts: 61 Thanks: 7 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?
 September 3rd, 2016, 08:35 AM #2 Member   Joined: Jan 2016 From: United States Posts: 61 Thanks: 7 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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### stumbling robot pascals triangle

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