How To Use Π Product Notation

A brief tutorial

What is Pi Notation? What does Π mean? Pi Product Notation is a handy way to express products, as Sigma Notation expresses sums. Here, we’ll present the notation with some applications.

Figure 1 shows how to express a factorial using Pi Product Notation. The index is given below the Π symbol. We multiply the expression to the right of the Π as many times as given by the number above the Π. With each iteration, we increase the index by 1.

Using Pi Product Notation to represent a factorial is not an efficient application of the notation. We already have a more concise notation for the factorial operation.

We can represent the function, sin x as an infinite product. Here, Pi Product Notation comes in handy.

The product continues indefinitely. It approaches sin x as we multiply each factor.

Figure 4

Figure 4 compares the graphs of three partial products. Each product builds on the prior by adding another factor. Each factor differs by an increment of the coefficient to π in the denominator.

We close with a challenge.

Here is the definition of a binomial coefficient using Pi Product Notation. Can you show why this definition is correct?