Question

Thực hiện phép tính sau một cách nhanh chóng :
\(\text{D=2^100-2^99-2^98-2^97-...-2^2-2-1}\)

Answer 1

dấu này ^ là dấu mũ hả bn

Answer 2

\(D=2^{100}-2^{99}-2^{98}-2^{97}-...-2^2-2-1\)

\(D=2^{100}-\left(2^{99}+2^{98}+2^{97}+...+2^2+2+1\right)\)

Đặt \(A=2^{99}+2^{98}+2^{97}+...+2^2+2+1\)

\(2A=2^{100}+2^{99}+2^{98}+...+2^3+2^2+2\)

\(2A-A=\left(2^{100}+2^{99}+2^{98}+...+2^3+2^2+2\right)-\left(2^{99}+2^{98}+2^{97}+...+2^2+2+1\right)\)

\(A=2^{100}-1\)

\(\Rightarrow D=2^{100}-\left(2^{100}-1\right)=2^{100}-2^{100}+1=0+1=1\)