Hi,

I was just playing around end ended up trying to find a closed form of the following sum,

$\displaystyle

\sum^{n-1}_{i=1} i(n-i)$

Writing it out I get,

$\displaystyle 1(n-1)+2(n-2)+3(n-3)+\cdots+ (n-1)(1)$

which is,

$\displaystyle 2(n-1)+2(n-2)+3(n-3)\cdots+ (n-2)(2)$

which is,

$\displaystyle 2(n-1)+4(n-2)+3(n-3)\cdots (n-3)(3)$ and so on...

I'm not sure what to make of this though. Could someone help me out finding a closed form for this sum?