Câu hỏi của Lyn Lee

Question

Thực hiện phép tính:

2100-299+298-297+...+22

Lightning Farron · Accepted Answer

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

$2A=2\left(2^2-2^3+2^4-...-2^{97}+2^{98}-2^{99}+2^{100}\right)$

$2A=2^3-2^4+...+2^{99}-2^{100}+2^{101}$

$2A+A=\left(2^3-2^4+...+2^{101}\right)+\left(2^2-2^3+...+2^{100}\right)$

$3A=2^{101}+4\Rightarrow A=\dfrac{2^{101}+4}{3}$Câu trả lời: $A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2$

$2A=2\left(2^2-2^3+2^4-...-2^{97}+2^{98}-2^{99}+2^{100}\right)$

$2A=2^3-2^4+...+2^{99}-2^{100}+2^{101}$

$2A+A=\left(2^3-2^4+...+2^{101}\right)+\left(2^2-2^3+...+2^{100}\right)$

$3A=2^{101}+4\Rightarrow A=\dfrac{2^{101}+4}{3}$

Đại số lớp 7