Tag Archives: big sigma

Big Sigma and Big Pi

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In this post we will look at some familiar mathematical notation in order to make it possible to read formulas we come across. I have assumed that the reader is familiar with how addition, multiplication, subtraction, division, and exponentiation are represented and what they mean. They will be the building blocks of other kinds of notation.

In a previous post we learned about the binomial coefficient and consequently what the factorial function is. There are lots of unfamiliar sorts of notation in mathematics, though.

Today we will look at the summation and product functions, represented by the big sigma and big pi notation. They’re frequently found in formulas. Let’s take a look at them.

Big Sigma
\displaystyle \sum_{a=i}^{n}(a)

Big Pi
\displaystyle \prod_{a=i}^{n}(a)

The notation indicates that we take each value of a from the initial value at the bottom straight through to the maximum value n, do the equation in parenthesis, and then either add together the results or multiply together the results.

It is easier to follow if we expand them.

Here is summation expanded to simple addition.
\displaystyle \sum_{a=0}^{4}(a) = 0+1+2+3+4 = 10

Now summation that involves an actual equation.
\displaystyle \sum_{a=0}^{4}(a^2-3) = (0^2-3)+(1^2-3)+(2^2-3)+(3^2-3)+(4^2-3)
. . . which becomes . . .
\displaystyle \sum_{a=0}^{4}(a^2-3) = (-3)+(-2)+(1)+(6)+(11)
. . . which becomes . . .
\displaystyle \sum_{a=0}^{4}(a^2-3) = 13

Exactly the same thing is done with the big pi symbol.