Let denote the sum of terms of an arithmetic progression (A.P.) whose . term is and the common difference is . Let and for The sum is...

Let V_{r} denote the sum of 1^{{st}{~}}r terms of an arithmetic progression (A.P.) whose 1^{{st}{~}} . term is r and the common difference is 2r - 1. Let T_{r} = V_{r + 1} - V_{r} and Q_{r} = T_{r + 1} - {T}_{r} for r = 1,2, The sum V_{1} + V_{2} + + V_{n} is: Sequence & Series (Mathematics)

Let

V_{r}

denote the sum of

1^{\text{st}\text{~}}r

terms of an arithmetic progression (A.P.) whose

1^{\text{st}\text{~}}

. term is

r

and the common difference is

2r - 1

. Let

T_{r} = V_{r + 1} - V_{r}

and

Q_{r} = T_{r + 1} - {T}_{r}

for

r = 1,2,\ldots

The sum

V_{1} + V_{2} + \ldots + V_{n}

\frac{n}{2}(n + 1)\left( 3n^{2} - n + 1 \right)

\frac{n}{12}(n + 1)\left( 3n^{2} + n + 2 \right)

\frac{n}{2}\left( 2n^{2} - n + 1 \right)

\frac{1}{3}\left( 2n^{3} - 2n + 3 \right)