Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Prove that : $n! ≥ (⌈n/2⌉)^{⌈n/2⌉}$

share|improve this question
    
Hint: Count it. How many integers satisfies $k\ge n/2$? –  tetori Feb 3 '13 at 8:57
1  
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. If this is homework, please add the homework tag; people will still help, so don't worry. 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
add comment

2 Answers

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

share|improve this answer
add comment

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

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.