Is there a simple formula for this sum?
$$\sum_{k=0}^nk(nk)=0\cdot n+1\cdot (n1)+2\cdot(n2)+\cdots+(n1)\cdot 1+n\cdot 0$$
It looks kind of familiar .. something to prove with induction in a proof writing class.
Thanks
Help with a finite sum

 Posts: 6
 Joined: Sat Oct 10, 2009 7:41 pm
Re: Help with a finite sum
Distribute the k, break into difference of two sums... see what you can do.
Re: Help with a finite sum
$$\sum_{k=0}^{n}k(nk)=n\sum_{k=0}^{n}k\sum_{k=0}^{n}k^2=\frac{n^2(n+1)}{2}\frac{n(n+1)(2n+1)}{6}=\frac{(n1)n(n+1)}{6}$$