# How to calculate arithmetic series?

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Susi D on 20 Nov 2011
Hi, I am new to mathlab. I want to evaluate an array and don't know how to do it with mathlab. Here are the two of the examples: n Sigmma notation i = i=1
n Signma notation i^2= i=1
Note: sigma notation means sums
Thanks. Susi
##### 2 CommentsShowHide 1 older comment
Grzegorz Knor on 21 Nov 2011
@Susi,look at symsum:
http://www.mathworks.com/help/toolbox/symbolic/symsum.html

David Young on 21 Nov 2011
Does your first example look like this:
n
SUM i
i=1
and your second example look like this:
n
SUM i^2
i=1
where I'm using SUM to stand for a capital sigma symbol?
If so, you would evaluate them in MATLAB like this:
n = 100; % set n to whatever value you need
i_vector = 1:n;
s1 = sum(i_vector);
s2 = sum(i_vector.^2);
To understand these examples, it's essential to look up the colon ( : ) operator in the introductory documentation or your textbook, as it's at the core of how this kind of operation is usually done. Also look at the documentation for the sum function, and for the .^ operator.
Jan on 21 Nov 2011
The elements of arithmetic series have a constant difference. Therefore (i_vector.^2) is not an arithmetic series.
"sum(1:n)" and "sum((1:n).^2" can be calculated without creating "1:n" explicitely, which is much cheaper for large n.

Susi D on 22 Nov 2011
Hi Guys, Thanks for your input=)You have been a great help. Yes, David, those are what I meant: n SUM i i=1
and
n SUM i^2 i=1
And Jan, hmmm....ya....I just remembered that arithmetic series shouldn't have ^2 =)
Best Regards =) Susi D

Susi D on 22 Nov 2011
Opps sorry, I don't know why my typing became a mess when it was posted.
So, yes, I meant:
n
SUM i
i=1
and
n
SUM i^2
i=1