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The value of sum(r=1)^(10)r(n C(r))/(n ...

The value of `sum_(r=1)^(10)r(n C_(r))/(n C_(r-1)) `=

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`because (r.""^(n)C_(r))/(r.""^(n)C_(r-1))= (n-r +1)/(r) `
` therefore (r.""^(n)C_(r))/(r.""^(n)C_(r-1))= (n-r +1) `
`therefore sum_(r=1)^(n) (r.""^(n)C_(1))/(r.""^(n)C_(r-1)) = sum_(r=1)^(n) (n-r+1)= sum_(r=1)^(n) (n+1) -sum_(r=1)^(n)r `
` =(n+1).n-(n(n+1))/(2) = (n(n+1))/(2)`
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