Stirling's formula

For the sake of argument, let's say .

We know that the following is true:

However, we now claim the following:

This can be illustrated as follows:

Now, by evaluating the integral, we get the following:

We now divide both sides by  and take the limit as n→∞. We observe that both sides tend to 1. So, we have the following:

Stirling's formula states that as n→∞, the following is true:

Furthermore, we have the following: