# Sigma Notation

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

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

So Σ means to sum things up ...

### Sum What?

Sum whatever is after the Sigma:

Σ

n
so we sum n

### But What Values of n ?

The values are shown below
and above the Sigma:

4
Σ
n=1
n
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:

4
Σ
n=1
n = 1 + 2 + 3 + 4 = 10

Here it is in one diagram:

## More Powerful

But Σ can do more powerful things than that!

We can square n each time and sum the result:

4
Σ
n=1
n2 = 12 + 22 + 32 + 42 = 30

We can add up the first four terms in the sequence 2n+1:

4
Σ
n=1
(2n+1) = 3 + 5 + 7 + 9 = 24

We can use other letters, here we use i and sum up i × (i+1), going from 1 to 3:

3
Σ
i=1
i(i+1) = 1×2 + 2×3 + 3×4 = 20

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

5
Σ
i=3
ii + 1 = 34 + 45 + 56

There are lots more examples in the more advanced topic Partial Sums.

You can try some of your own with the Sigma Calculator.

## Why is it called "Sigma"

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

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