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Prove that : $n! ≥ (⌈n/2⌉)^{⌈n/2⌉}$

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closed as off-topic by ᴡᴏʀᴅs, Dan Rust, Hakim, Cookie, hardmath Jul 4 '14 at 0:47

This question appears to be off-topic. The users who voted to close gave this specific reason:

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Hint: Count it. How many integers satisfies $k\ge n/2$? – Hanul Jeon Feb 3 '13 at 8:57
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post. – Julian Kuelshammer Feb 3 '13 at 9:19

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

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

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