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 Stirlings formula for approximating large factorials The formula involves the irrational numbers p and e n 2n n n e n As an example, the exact value of 5 is 120, and Stirlings 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 Stirlings formula

Question: The factorial of a positive integer n can be computed as a product. n! = 1 2 3 g n Calculators

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.

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