Câu hỏi của Hà Công Minh Phi

Question

Tính b =2^ 100 -2^ 99 -...-2^ 3 -2^ 2 - 2

Bài tập Tất cả

Đoàn Đức Hà · Accepted Answer

$B=2^{100}-2^{99}-...-2^3-2^2-2$

$A=2^{99}+2^{98}+...+2^3+2^2+2$

$2A=2^{100}+2^{99}+...+2^4+2^3+2^2$

$2A-A=\left(2^{100}+2^{99}+...+2^4+2^3+2^2\right)-\left(2^{99}+2^{98}+...+2^3+2^2+2\right)$

$A=2^{100}-2$

Suy ra $B=2^{100}-A=2^{100}-\left(2^{100}-2\right)=2$

Câu trả lời:

$B=2^{100}-2^{99}-...-2^3-2^2-2$

$A=2^{99}+2^{98}+...+2^3+2^2+2$

$2A=2^{100}+2^{99}+...+2^4+2^3+2^2$

$2A-A=\left(2^{100}+2^{99}+...+2^4+2^3+2^2\right)-\left(2^{99}+2^{98}+...+2^3+2^2+2\right)$

$A=2^{100}-2$

Suy ra $B=2^{100}-A=2^{100}-\left(2^{100}-2\right)=2$