Câu hỏi của Tuan Duy

Question

cho A= 2 + 2² + 2³ + ...... + 2⁶³

...

Trần Quỳnh Mai · Accepted Answer

$A=2+2^2+2^3+...+2^{61}+2^{62}+2^{63}$

$A=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{61}+2^{62}+2^{63}\right)$

$A=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+...+2^{61}\left(1+2+2^2\right)$

$A=2.7+2^4.7+...+2^{61}.7$

$A=\left(2+2^4+...+2^{61}\right).7\Rightarrow A⋮7$

Vậy ...

Câu trả lời:

$A=2+2^2+2^3+...+2^{61}+2^{62}+2^{63}$

$A=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{61}+2^{62}+2^{63}\right)$

$A=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+...+2^{61}\left(1+2+2^2\right)$

$A=2.7+2^4.7+...+2^{61}.7$

$A=\left(2+2^4+...+2^{61}\right).7\Rightarrow A⋮7$

Vậy ...

Nguyễn Huy Tú · Answer

Ta có:

$A=2+2^2+2^3+...+2^{63}$

$\Rightarrow A=\left(2+2^2+2^3\right)+...+\left(2^{61}+2^{62}+2^{63}\right)$

$\Rightarrow A=2\left(1+2+2^2\right)+...+2^{61}\left(1+2+2^2\right)$

$\Rightarrow A=2.7+...+2^{61}.7$

$\Rightarrow A=\left(2+...+2^{61}\right).7⋮7$

$\Rightarrow A⋮7$

$\Rightarrowđpcm$