Summation help

[johnbobson]

Hello. I was wondering if someone could please explain the proper way to evaluate the following type of summation:

∑ [ i = negative number, positive number] i^2 = ?

Which one of the formulas below applies to this type of problem?

http://en.wikipedia.org/wiki/Summation

The only one that is similar is ∑ [ i = 0, positive number] i^2 = (1/6)(positive number)((positive number)+1)(2(positive number)+1)

But it starts from zero. Does it still apply if i starts at, for example, -5?

 

[MarkFL]

I would use (where \(\displaystyle a\le0\)):

\(\displaystyle \displaystyle \sum_{k=-a}^b k^2=\sum_{k=0}^a k^2+\sum_{k=0}^b k^2\)

 

[johnbobson]

I would use (where \(\displaystyle a\le0\)):

\(\displaystyle \displaystyle \sum_{k=-a}^b k^2=\sum_{k=0}^a k^2+\sum_{k=0}^b k^2\)

Thank you. If the limit starts at -a and goes to a then we have ∑ [ i =-a, a] i^2 = ∑ [ i =0, a] i^2 + ∑ [ i =0, a] i^2= 2* ∑ [ i =0, a] i^2
Is that correct?

 

[MarkFL]

Yes, that's right, you would just double the summation from 0 to a in that case.

 

[johnbobson]

Yes, that's right, you would just double the summation from 0 to a in that case.

Great. Thank you for clearing that up for me.