Câu hỏi của Nguyễn Đỗ Quang Anh

Question

(2¹¹+2¹⁰+2⁹+...2³+2²+2+1):(2⁸+2⁴+1)

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(Cái này chị mình nhờ gửi đấy)

Mysterious Person · Accepted Answer

$\dfrac{2^{11}+2^{10}+2^9+...+2^3+2^2+2+1}{2^8+2^4+1}$

$=\dfrac{\left(2^8+2^4+1\right)+\left(2^9+2^5+2\right)+\left(2^{10}+2^6+2^2\right)+\left(2^{11}+2^7+2^3\right)}{2^8+2^4+1}$

$=\dfrac{\left(2^8+2^4+1\right)+2\left(2^8+2^4+1\right)+2^2\left(2^8+2^4+1\right)+2^3\left(2^8+2^4+1\right)}{2^8+2^4+1}$

$=\dfrac{\left(1+2+2^2+2^3\right)\left(2^8+2^4+1\right)}{\left(2^8+2^4+1\right)}=1+2+2^2+2^3$

$=1+2+4+8=15$

Câu trả lời:

$\dfrac{2^{11}+2^{10}+2^9+...+2^3+2^2+2+1}{2^8+2^4+1}$

$=\dfrac{\left(2^8+2^4+1\right)+\left(2^9+2^5+2\right)+\left(2^{10}+2^6+2^2\right)+\left(2^{11}+2^7+2^3\right)}{2^8+2^4+1}$

$=\dfrac{\left(2^8+2^4+1\right)+2\left(2^8+2^4+1\right)+2^2\left(2^8+2^4+1\right)+2^3\left(2^8+2^4+1\right)}{2^8+2^4+1}$

$=\dfrac{\left(1+2+2^2+2^3\right)\left(2^8+2^4+1\right)}{\left(2^8+2^4+1\right)}=1+2+2^2+2^3$

$=1+2+4+8=15$