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:

Sigma Notation

More Powerful

But Σ can do more powerful things than that!

We can square n each time and sum the result:

n=1

n² = 1² + 2² + 3² + 4² = 30

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

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:

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:

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.

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

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