The factorial of a positive integer n can be computed as a product.

n! = 1 · 2 · 3 · g · n

Calculators and computers can evaluate factorials very quickly. Before the days of modern technology, mathematicians developed Stirling’s formula for approximating large factorials. The formula involves the irrational numbers p and e.

n! ≈ √2πn · nⁿ · e^-n

As an example, the exact value of 5! is 120, and Stirling’s formula gives the approximation as 118.019168 with a graphing calculator. This is “off” by less than 2, an error of only 1.65%.

Use a calculator to find the exact value of 10! and its approximation, using Stirling’s formula.