Prove that $n! ≥ (⌈n/2⌉)^{⌈n/2⌉}$

Question

Prove that : $n! ≥ (⌈n/2⌉)^{⌈n/2⌉}$

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user17762 · Answer 1 · 2013-02-03 08:59:20Z

up vote 1 down vote

$$n! \geq n(n-1)(n-2)(n-3) \cdots \lceil n/2 \rceil \geq (\lceil n/2 \rceil)^{\lceil n/2 \rceil}$$

answered Feb 3 at 8:59

user17762
76.1k8106230

ashley · Answer 2 · 2013-02-03 08:58:47Z

up vote 0 down vote

Hint: $2a*(2a-1)*(2a-2)*...*a*k > a^a$ where $k>0$.

answered Feb 3 at 8:58

ashley
5218

2 Answers