Câu hỏi của Nguyễn Hương Ly

Question

Rút gọn: A = $2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2$

jussia · Accepted Answer

$A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2$

$2A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2$

$2A+A=\left(2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\right)+\left(2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\right)$

$3A=2^{101}-2$

$A=\frac{2^{101}-2}{3}$

Câu trả lời:

$A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2$

$2A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2$

$2A+A=\left(2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\right)+\left(2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\right)$

$3A=2^{101}-2$

$A=\frac{2^{101}-2}{3}$

Trần Đức Thắng · Answer

A = 2^100 - 2^99 + 2^98 - 2^97 + ...+2^2 - 2

2A = 2^101 - 2^100 + 2^99 - 2^98 +.... +2^3 - 2^2

2A + A = 2^101 - 2^100 + 2^99 -2^98 + ...+2^3 - 2 ^ 2 + 2^100 - 2^99 + 2^98 - ...+2^2 - 2