Bonjour,
The problem i have follows from the definition of the binomial coefficient:
$\frac{n(n-1)...(n-k+1)}{k!} = {n \choose k}$
For 0$\leq{i}$ and i less than k, we observe that:
$\frac{n-i}{k-i}\geq\frac{n}{k}$
Is there a simple and intuitive arithmetic proof of this inequality ?
This inequality is sometimes used to prove that:
$(\frac{n}{k})^k\leq {n \choose k}$