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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 Sigmameans 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,
so that 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

 

And this next one means "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!

Why is it called "Sigma"

Sigma is Greek

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

 

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