For all \(k \in \mathbb{N}\), we have
\[ \left(\frac{k}{e}\right)^k \;\leq\; k! \;\leq\; k^k. \]Link Link to heading
- proof
- factorial
- \(k!< (\frac{k+1}{2})^k\) (see (0x691b30d1) )
For all \(k \in \mathbb{N}\), we have
\[ \left(\frac{k}{e}\right)^k \;\leq\; k! \;\leq\; k^k. \]