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

The value of `sum_(r=1)^(10) r. (""^(n)C_(r))/(""^(n)C_(r-1)` is equal to

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We have
`underset(r=1)overset(10)(sum)r*(.^(n)C_(r))/(.^(n)C_(r-1))=underset(r=1)overset(10)(sum)r*((n!)/(r!(n-r)!))/((n!)/((r-1)!(n-r+1)!))=underset(r=1)overset(10)(sum)r((n-r+1)/(r))`
`underset(r=1)overset(10)(sum)(n-r+1)=n+(n-1)+(n-2)+ . . . .+(n-9)`
`=10n-(1+2+3+ . . .+9)`
`=10n-9xx5=5(2n-9)`
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