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Let Vr denote the sum of the first r ter...

Let `V_r` denote the sum of the first r terms of an arithmetic progression (AP) whose first term is r and the common difference is `(2r-1). Let `T_r=V_(r+1)-V_r-2 and Q_r =T_(r+1)-T_r for r=1,2` .The sum V1+V2+...+Vn is

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The correct Answer is:
B
Here, `V_(r) = (r)/(2) [2r + (r -1) (2r -1)] = (1)/(2) (2r^(3) - r^(2) + r)`
`:. Sigma V_(r) = (1)/(2) [2Sigma r^(3) - Sigma r^(2) + Sigma r]`
`= (1)/(2) [s{(n (n+1))/(2)}^(2) - (n (n+1) (2n +1))/(6) + (n(n+1))/(2)]`
`rArr = (n(n +1))/(12) [3n (n +1) - (2n +1) + 3]`
`= (1)/(12) n (n +1) (3n^(2) + n +2)`
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