The factorial of a positive integer n can be computed as a product. n! = 1
Question:
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%.
Subtract the smaller value from the larger value in Exercise 59. Divide it by 10! and convert to a percent. What is the percent error to three decimal places?
Exercise 59.
Use a calculator to find the exact value of 10! and its approximation, using Stirling’s formula.
Step by Step Answer:
College Algebra
ISBN: 978-0134697024
12th edition
Authors: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels