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

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

Grade:11

1 Answers

Arun
25763 Points
3 years ago
n+1CrLHS=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)!]=
hence proved

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