Re: summation help

On Mon, 11 Apr 2005, jimbo wrote:

> I currently have the following summation:
> the summation of ( (N-L+1)(L-1) ) from L = 2 to N.
>
> I am trying to reduce this to some form something like:
> the summation of (N*L-L^2) from L=1 to N-1...
>

sum(j=1..n) (n - j + 1)(j - 1)
= sum(j=1..n)(nj - j^2 + j - n + j - 1)
= sum_j [(n+2)j - j^2 - (n+1)]
= (n+2).sum_j j - sum_j j^2 - n(n+1)

> Does anyone have any suggestions?
>
Find sum_j j and sum_j j^2.
.