Help with a finite sum
Posted: Sat Mar 20, 2010 9:28 am
Is there a simple formula for this sum?
$$\sum_{k=0}^nk(n-k)=0\cdot n+1\cdot (n-1)+2\cdot(n-2)+\cdots+(n-1)\cdot 1+n\cdot 0$$
It looks kind of familiar .. something to prove with induction in a proof writing class.
Thanks
$$\sum_{k=0}^nk(n-k)=0\cdot n+1\cdot (n-1)+2\cdot(n-2)+\cdots+(n-1)\cdot 1+n\cdot 0$$
It looks kind of familiar .. something to prove with induction in a proof writing class.
Thanks