Originally Posted by

**NathanBUK** Hi the problem that I have is to show $\displaystyle \sum(r^2-r)=kn(n+1)(n-1)$

where $\displaystyle k$ is a rational number. (Also on the sum sign there is $\displaystyle n$ on top and $\displaystyle r=1$ on bottom.

I know what I need to do to start which is show $\displaystyle \sum r^2-\sum r=\frac{1}{6}n(n+1)(2n+1)-\frac{1}{2}n(n+1)$

but my problem is I find it really hard to realise where the common factors are and what I should, if anything expand anywere. I would be really greatful if someone could post a step by step method on how they would do this explaing what has been extracted and what has been expanded. I know its seems alot but I would be really greatful. Thankyou!