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Find the sum of sum(r=1)^n(r^n Cr)/(^n C...

Find the sum of `sum_(r=1)^n(r^n C_r)/(^n C_(r-1)` .

Text Solution

Verified by Experts

`underset(r=1)overset(n)sum(r.^(n)C_(r))/(.^(n)C_(r-1))=underset(r=1)overset(n)sumr(n-r+1)/(r)`
`= (n+1)underset(r=1)overset(n)sum1-underset(r=1)overset(n)sumr`
`=n(n+1)-(n(n+1))/(2)`
`= (n(n+1))/(2)`
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