(Steps Shown) (a) Using the property of the Gamma function that \Gamma (x)≈ (x/e)^x√(2pi)/(x) prove Stirling’s approximation: n!≈ (n/e)^n√2pi
Question: (a) Using the property of the Gamma function that
\(\Gamma \left( x \right)\approx {{\left( \frac{x}{e} \right)}^{x}}\sqrt{\frac{2\pi }{x}}\)
prove Stirling’s approximation:
\(\,\,n!\approx \,{{\left( \frac{n}{e} \right)}^{n}}\sqrt{2\pi n}\)
(b) Evaluate the ratio of n! and the approximation of n! above for n ranging from 10 to 150 in intervals of size 10.
(c) Use Stirling’s approximation to estimate 10!
Deliverable: Word Document 
