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Proposition: Inequality between Powers of $2$ and Factorials

For all natural numbers $n\ge 4$, the following inequality holds $$2^n\le n!.$$

Example

For $n < 4$, we have $$\begin{array}{rrcc}n&2^n&n !&\text{comparison}\\ 0&1&1& = \\ 1&2&1& > \\ 2&4&2& > \\ 3&8&6& > \\ \end{array}$$

Table of Contents

Proofs: 1

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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983