SOLUTION: Prove that the following relationship is true: nCr + nC(r+1) ?=? (n+1)C(r+1) Use the least common denominator method.

Question 940228: Prove that the following relationship is true:
nCr + nC(r+1) ?=? (n+1)C(r+1)
Use the least common denominator method.
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

nCr + nC(r+1) ?=? (n+1)C(r+1)
------------------------------------

(1)   nCr = 

(2)   nC(r+1) =  = 

(3)   (n+1)C(r+1) =  =  = 

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

nCr + nC(r+1) = 



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

 

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

 

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

 

 













(n+1)C(r+1)

Edwin

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