Số tự nhiên n thỏa mãn C 1 n + 2.(C 2 n ) + 3 (C 3 n)

* Hướng dẫn giải

Đáp án C.

$\begin{array}{l}{\left(1+x\right)}^n=C_n^0+C_n^{1}x+C_n^2{x}^2+C_n^3{x}^3+\mathrm{...}+C_n^n{x}^n\\ \to n{\left(1+x\right)}^{n-1}=C_n^1+2C_n^{2}x+3C_n^3{x}^2+\mathrm{...}+n{C}_n^n{x}^{n-1}\end{array}$

$\begin{array}{l}\stackrel{x=1}{\to }n{.2}^{n-1}=C_n^1+2C_n^{2}x+3C_n^3{x}^2+\mathrm{...}+n{C}_n^n{x}^{n-1}\\ =11264\to n=11\in \left[10;12\right].\end{array}$