Đáp án:
\(2^{10}\)
Giải thích các bước giải:
$\begin{array}{l}
{\left( {1 + 1} \right)^{11}} = C_{11}^0 + C_{11}^1 + C_{11}^2 + C_{11}^3 + C_{11}^4 + C_{11}^5\\
+ C_{11}^6 + C_{11}^7 + C_{11}^8 + C_{11}^9 + C_{11}^{10} + C_{11}^{11}\\
\Leftrightarrow {2^{11}} = C_{11}^{11} + C_{11}^{10} + C_{11}^9 + C_{11}^8 + C_{11}^7 + C_{11}^6\\
+ C_{11}^6 + C_{11}^7 + C_{11}^8 + C_{11}^9 + C_{11}^{10} + C_{11}^{11}\\
\Leftrightarrow {2^{11}} = 2\left( {C_{11}^6 + C_{11}^7 + C_{11}^8 + C_{11}^9 + C_{11}^{10} + C_{11}^{11}} \right)\\
\Leftrightarrow C_{11}^6 + C_{11}^7 + C_{11}^8 + C_{11}^9 + C_{11}^{10} + C_{11}^{11} = {2^{11}}:2\\
\Leftrightarrow C_{11}^6 + C_{11}^7 + C_{11}^8 + C_{11}^9 + C_{11}^{10} + C_{11}^{11} = {2^{10}}
\end{array}$
