Câu hỏi của Yến Nhi Lê Thị

Question

A = 2 + 2⁰ + 2³ + 2⁵ + ..... + 2⁹⁹

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Nguyễn Huy Tú · Accepted Answer

$A=2+2^0+2^3+2^5+...+2^{99}$

$\Rightarrow4A=2^3+2^2+2^5+2^7+...+2^{101}$

$\Rightarrow4A-A=\left(2^3+2^2+...+2^{101}\right)-\left(2+2^0+...+2^{99}\right)$

$\Rightarrow3A=2^3+2^2+2^{101}-\left(2^0+2\right)$

$\Rightarrow3A=12+2^{101}-3$

$\Rightarrow A=\frac{2^{101}+9}{3}$

Câu trả lời:

$A=2+2^0+2^3+2^5+...+2^{99}$

$\Rightarrow4A=2^3+2^2+2^5+2^7+...+2^{101}$

$\Rightarrow4A-A=\left(2^3+2^2+...+2^{101}\right)-\left(2+2^0+...+2^{99}\right)$

$\Rightarrow3A=2^3+2^2+2^{101}-\left(2^0+2\right)$

$\Rightarrow3A=12+2^{101}-3$

$\Rightarrow A=\frac{2^{101}+9}{3}$