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

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