Đặt \(A=2^{10}-2^9-...-2-1\)
\(A=2^{10}-\left(2^9+...+2+1\right)\)
\(A=2^{10}-\left(1+2+...+2^9\right)\)
Đặt \(B=1+2+...+2^9\)
\(2B=2+2^2+...+2^{10}\)
\(2B-B=\left(2+2^2+...+2^{10}\right)-\left(1+2+...+2^9\right)\)
\(B=2^{10}-1\)
Thay B vào A ta có:
\(A=2^{10}-\left(2^{10}-1\right)=2^{10}-2^{10}+1=1\)
