SOLUTION: Show that the way in which the entries in Pascal's triangle are formedby adding "above left" and "above right' is consistent with the following statement; nCr-1 +nCr =n+1Cr Us

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Question 947191: Show that the way in which the entries in Pascal's triangle are formedby adding "above left" and "above right' is consistent with the following statement;
nCr-1 +nCr =n+1Cr
Use the fact that nCr = n!/(n-r)!r! to show that the above statement is true.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Question 940228
nC(r-1) + nC(r) ?=? (n+1)Cr
------------------------------------

(1)   nCr = 

(2)   nC(r-1) =  = 

(3)   (n+1)Cr =  = 

---------------------------
We want to prove that expression(2) + expression(1) = expression(3)

nC(r-1) + nCr =



Substitute (n-r+1)(n-r)! for (n-r+1)! and r(r-1)! for r!



LCD = r(r-1)!(n-r+1)(n-r)!



replace r(r-1)! by r! and replace (n-r+1)(n-r) by (n-r+1)!















(n+1)Cr

Edwin
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