Stirling's Formula/Refinement/Examples/8

Example of Use of the Refinement to Stirling's Formula
The factorial of $8$ is given by the refinement to Stirling's formula as:
 * $8! \approx 40 \, 318$

which shows an error of about $0.005 \%$.

Proof
We have that by the usual calculation:
 * $8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40 \ 320$

Hence: