Câu hỏi của Phạm Lê Khánh Nhi

Question

Rút gọn biểu thức sau

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

Lê Nhật Phương · Accepted Answer

$\text{M}=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2$

$\Rightarrow2\text{M}=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2$

$\Rightarrow2\text{M}+\text{M}=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2+2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2$

$\Rightarrow3\text{M}=2^{201}-2$

$\Rightarrow\text{M}=\dfrac{2^{201}-2}{3}$Câu trả lời: $\text{M}=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2$

$\Rightarrow2\text{M}=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2$

$\Rightarrow2\text{M}+\text{M}=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2+2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2$

$\Rightarrow3\text{M}=2^{201}-2$

$\Rightarrow\text{M}=\dfrac{2^{201}-2}{3}$

Chương I : Số hữu tỉ. Số thực