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D

- Hướng dẫn giải

Đáp án D

 Xét

 $$\begin{gathered} {\left(1+x\right)}^{2016}=C_{2016}^0+C_{2016}^{1}x+C_{2016}^2{x}^2+C_{2016}^3{x}^3 \\ +\mathrm{...}+C_{2016}^{2016}{x}^{2016} \end{gathered}$$

chọn x=1 ta có

$\begin{array}{l}{\left(1+1\right)}^{2016}=C_{2016}^0+C_{2016}^1+C_{2016}^2+C_{2016}^3+\mathrm{...}+C_{2016}^{2016}\\ \iff 2^{2016}-C_{2016}^0=C_{2016}^1+C_{2016}^2+C_{2016}^3+\mathrm{...}+C_{2016}^{2016}\\ \iff C_{2016}^1+C_{2016}^2+C_{2016}^3+\mathrm{...}+C_{2016}^{2016}=2^{2016}-1\end{array}$