\(A=2^{2017}-\left(2^{2016}+...+2^1+1\right)\\ \)
Đặt \(B=1+2+...+2^{2016}\)
\(\Rightarrow2.B=2+2^2+...+2^{2017}\\ \Rightarrow2.B-B=\left(2+2^2+...+2^{2017}\right)-\left(1+2+...+2^{2016}\right)\\ \Rightarrow B=2^{2017}-1\\ \Rightarrow A=2^{2017}-B=2^{2017}-2^{2017}+1=1\)