Factorial estimate
Task number: 3852
Prove the following lower bound on the factorial: \(e \cdot \left(\frac{n}{e}\right)^n \leq n!\)
Hint
Either by the integration or by the induction. Use \(1+x \leq e^x\) in the denominator.
Prove the following lower bound on the factorial: \(e \cdot \left(\frac{n}{e}\right)^n \leq n!\)
Either by the integration or by the induction. Use \(1+x \leq e^x\) in the denominator.