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Sequences and Series question

2007 · Shift 1 · Q36

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JEE Advanced
Mathematics
Sequences and Series
2007 · Shift 1 · Q36

Sequences and Series question

2007 · Shift 1 · Q36

JEE AdvancedMathematicsSequences and SeriesMCQ+3 / −1

Let V

_r

denote the sum of the first r terms of an arithmetic progression (A.P.) 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 V

_1

+ V

_2

+ ... + V

_n

is

A
${1 \over {12}}n(n + 1)(3{n^2} - n + 1)$
B
${1 \over {12}}n(n + 1)(3{n^2} + n + 2)$
C
${1 \over 2}n(2{n^2} - n + 1)$
D
${1 \over 3}(2{n^3} - 2n + 3)$

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