Câu hỏi của Lê Huyền Linh

Question

B=2¹⁰⁰-2⁹⁹+2⁹⁸-2⁹⁷....-2³+2²-2+1

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Đoàn Đức Hà · Accepted Answer

$B=2^{100}-2^{99}+2^{98}-2^{97}+...-2^3+2^2-2+1$

$2B=2^{101}-2^{100}+2^{99}-2^{98}+...-2^4+2^3-2^2+2$

$B+2B=\left(2^{100}-2^{99}+2^{98}-2^{97}+...-2^3+2^2-2+1\right)+\left(2^{101}-2^{100}+...+2\right)$

$3B=2^{101}+1$

$B=\frac{2^{101}+1}{3}$

Câu trả lời:

$B=2^{100}-2^{99}+2^{98}-2^{97}+...-2^3+2^2-2+1$

$2B=2^{101}-2^{100}+2^{99}-2^{98}+...-2^4+2^3-2^2+2$

$B+2B=\left(2^{100}-2^{99}+2^{98}-2^{97}+...-2^3+2^2-2+1\right)+\left(2^{101}-2^{100}+...+2\right)$

$3B=2^{101}+1$

$B=\frac{2^{101}+1}{3}$