Đặt
$a_k=C^k_{2011}=\frac{2011!}{k!(2011-k)!}$ và
$a_{k+1}=C^{k+1}_{2011}=\frac{2011!}{(k+1)!(2011-k)!}$
$\frac{a_{k+1}}{a_k}=\frac{C^{k+1}_{2011}}{C^k_{2011}}=\frac{2011-k}{k+1}$
*Khi $x_n
> 0 \Rightarrow a_0 < a_1 <…<a_{1005} < a_{1006}$
*Khi $\frac{a_{k+1}}{a_k}<1
\Leftrightarrow \frac{2011-k}{k+1}<1 \Leftrightarrow k>1005$
$\Rightarrow
a_{2011}<a_{2010}<…<a_{1007}<a_{1006}$
Suy ra: $max(C^k_{2011})=max(a_k)=a_{1006}$
khi $k=1006$.