Waste less time on Facebook — follow Brilliant.
×

A Refined Approximation of \(n!\)

Demonstrate, for \(n > 0\), the bound \[\sqrt { 2\pi n } { \left( \frac { 1 }{ e } \left( n+\frac { 1 }{ 12n } \right) \right) }^{ n } < n! < \sqrt { 2\pi n } { \left( \frac { n }{ e } \right) }^{ n }{ e }^{ \frac { 1 }{ 12n } }.\]

I discovered this asymptotic bound of n factorial in 2010.

Solution

To see a full demonstration, you can read it at my blog.

Check out my other notes at Proof, Disproof, and Derivation

Note by Steven Zheng
2 years, 8 months ago

No vote yet
1 vote

Comments

There are no comments in this discussion.

×

Problem Loading...

Note Loading...

Set Loading...