# Thread: Summation Closed Forms

1. ## Summation Closed Forms

Find the closed form for:
$\sum_{i=-1}^{n}i$

It's given that the closed form $\sum_{i=1}^{n}i = (n(n+1))/2$ so we can write:
$\sum_{i=-1}^{n}i = (-1) + 0 + \sum_{i=1}^{n}i = (n(n+1))/2$

...

$( (n+2)(n-1) )/2$

I understand the final closed form answer but could someone explain where the terms (-1) + 0 come from on the first line. I'm assuming the -1 comes from the lower bounds of the summation..

2. $\sum\limits_{i=-1}^{n}{i}=\sum\limits_{i=1}^{n+2}{(i-2)}=\frac{(n+2)(n+3)}{2}-2(n+2)=\frac{(n+2)(n-1)}{2}.$

3. Thanks.