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Prove : n! / r!(n-r)! + n! / (r-1)(n-r+1)! = (n+1)! / r! ( n-r+1)!

Prove :
n! / r!(n-r)!  + n! / (r-1)(n-r+1)!  = (n+1)! / r! ( n-r+1)!

Grade:9

1 Answers

Faiz
107 Points
7 years ago
LHS=n!/[r!(n-r)!]+n!/[(r-1)!(n-r+1)!]=n!/[r(r-1)!(n-r)!]+ n!/[(r-1)!(n-r+1)(n-r)!]=n!/[(r-1)!(n-r)!]{[1/r]+[1/(n-r+1)]}=n!/[(r-1)!(n-r)!]{(n+1)/r(n-r+1)}=(n+1)n!/[r(r-1)!(n-r+1)(n-r)!]=(n+1)!/[r!(n-r+1)!]=n+1Crans

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