Câu hỏi của Phạm Minh Đức

Question

CMR:A=21+22+23+24+...+22010 chia hết cho 3

Nguyễn Nam · Accepted Answer

$A=2^1+2^2+2^3+2^4+....+2^{2009}+2^{2010}$

$\Rightarrow A=\left(2^1+2^2\right)+\left(2^3+2^4\right)+....+\left(2^{2009}+2^{2010}\right)$

$\Rightarrow A=2\left(1+2\right)+2^3\left(1+2\right)+....+2^{2009}\left(1+2\right)$

$\Rightarrow A=2.3+2^3.3+....+2^{2009}.3$

​$\Rightarrow A=3\left(2+2^3+....+2^{2009}\right)⋮3\left(dpcm\right)$​Câu trả lời: $A=2^1+2^2+2^3+2^4+....+2^{2009}+2^{2010}$

$\Rightarrow A=\left(2^1+2^2\right)+\left(2^3+2^4\right)+....+\left(2^{2009}+2^{2010}\right)$

$\Rightarrow A=2\left(1+2\right)+2^3\left(1+2\right)+....+2^{2009}\left(1+2\right)$

$\Rightarrow A=2.3+2^3.3+....+2^{2009}.3$

​$\Rightarrow A=3\left(2+2^3+....+2^{2009}\right)⋮3\left(dpcm\right)$​

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