$C^n_{2n+k}.C^n_{2n-k}\leq (C^n_{2n})^2$
$\Leftrightarrow [(n+k+n)..(n+k+2)(n+k+1)][(n-k+n)..(n-k+2)(n-k+1)]\leq [(n+n)..(n+2)(n+1)]^2$ $(\star)$
Ta sẽ chứng minh $(\star)$ đúng theo Cauchy, thật vậy:
$\prod_{i=1}^{n}(n+k+i)(n-k+i)\leq \prod_{i=1}^{n}(n+i)^2$ (đpcm)