Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $n$ be a natural number, $m\in [-n, n]$. Let $p=0,\ldots, \frac{n+m}{2}$.

Show, that for all $p$, $$ {n \choose \left[{\frac{n+m}{2}}\right]}\geq \frac{2^{n+1/2}}{\sqrt{n-p/2}}. $$

Thank you for your help.

share|cite|improve this question
What is this $N$ that suddenly pops up? – Jonathan Christensen Jan 28 '13 at 22:31
@Alex, do you mean $\forall n,m>N$? – user45099 Jan 28 '13 at 22:41
Sorry it suppose to be $n$ instead of $N$. – Alex Jan 28 '13 at 23:01
If $m=n$ and $p={n+m\over 2}=n$, then the right hand side is infinite.... – Byron Schmuland Jan 29 '13 at 1:02
Sorry, its one more typo-it should be $p/2$ under the square root. – Alex Jan 29 '13 at 1:55

Your Answer


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

Browse other questions tagged or ask your own question.