The value of ` sum_(r=1)^(49)(2r^(2) - 48r +1)/((50-r).""^(50)C_(r))` is `"_____"`.

Answer

2499

Explanation

`underset(r=1)overset(49)sum(2r^(2)-48r+1)/((50-r)..^(50)C_(r))= underset(r=1)overset(49)sum((r+1)^2-r(50-r))/((50-r).^(50)C_(r))`
`= underset(r=1)overset(49)sum(((r+1^(2)))/((50-r)..^(50)C_(r))-(r)/(.^(50)C_(r)))`
`=underset(r=1)overset(49)sum((r+1)/((50-r)((.^(50)C_(r))/(r+1)))-(r)/(.^(50)C_(r)))`
`=underset(r=1)overset(49)sum((r+1)/(.^(50)C_(r+1))-(r)/(.^(50)C_(r)))`
`=(50)/(.^(50)C_(50))-(r)/(.^(50)C_(1))`
`= 50 - 1/50`