Sigma Notation

Sigma   This symbol (called Sigma) means "sum up"

I love Sigma, it is fun to use, and can do many clever things.

So Sigma means to sum things up ...

Sum What?

Sum whatever appears after the Sigma:

  Sigma

so we sum n

But What is the Value of n ?

The values are shown below
and above the Sigma:

  Sigma

it says n goes from 1 to 4,
which is 1, 2, 3 and 4

OK, Let's Go ...

So now we add up 1,2,3 and 4:

  Sigma

Here it is in one diagram:

Sigma Notation

More Powerful

But Σ can do more powerful things than that!

You could square n each time and sum the result:

Sigma

You could "add up the first four terms in the sequence 2n+1":

Sigma

And you don't have to use n. Here we use i and sum up i × (i+1), going from 1 to 3:

Sigma

And you can start and end with any number. Here we go from 3 to 5:

Sigma

 


Try some of your own with the Sigma Calculator.

 

And now you get the idea, you might like to read the more advanced topic Partial Sums.

Why is it called "Sigma"

Sigma is Greek

Sigma is the upper case letter S in Greek. And S stands for Sum.