$1 \times 3 + 2 \times 5 + 3 \times 7 + \cdots$

$1 \times 5 + 2 \times 8 + 3 \times 11 + \cdots$

$1 \times 2 + 2 \times 5 + 3 \times 8 + \cdots$

$1 \times 3 \times 5 + 2 \times 4 \times 6 + 3 \times 5 \times 7 + \cdots$

$1 \times 2 \times 4 + 2 \times 3 \times 7 + 3 \times 4 \times 10 + \cdots$

$2^2 + 4^2 + 6^2 + \cdots$

$3^2 + 6^2 + 9^2 + \cdots$

$4 \times 1^2 + 7 \times 2^2 + 10 \times 3^2 + \cdots$

$3 + (3+7) + (3+7+11) + \cdots$

$1^2 + (1^2 + 2^2) + (1^2 + 2^2 + 3^2) + \cdots$

$1^2 - 2^2 + 3^2 - 4^2 + \cdots + (2n-1)^2 - (2n)^2$

$\dfrac{1^2}{1} + \dfrac{1^2 + 2^2}{2} + \dfrac{1^2 + 2^2 + 3^2}{3} + \cdots$ to $n$ terms

$5n^2 + 2n + 3$

$n^2 + 2n - 3$

$3n^2 + 5n + 2$

$n^2 + n - 2$