How can I simplify $1\times 2 + 2 \times 3 + .. + (n-1) \times n$ progression? I have a progression that goes like this:
$$1\times 2 + 2 \times 3 + .. + (n-1) \times n$$
Is there a way I can simplify it?

Hint. You have
$$
(n^3-n)-\left((n-1)^3-(n-1)\right)=3\times(n-1)\times n
$$ and the sum is telescoping.
