Câu hỏi của Nguyễn yến nhi

Question

Cho A=1+2+2^2+2^3+...+2^2017. Chứng minh rằng A=2^2018 -1.

❖︵Ňɠυүễη Çɦâυ Ƭυấη Ƙїệт♔ · Accepted Answer

$A=1+2+2^2+2^3+...+2^{2017}$

$\Rightarrow2A=2+2^2+2^3+2^4+...+2^{2018}$

$\Rightarrow2A-A=\left(2+2^2+2^3+...+2^{2018}\right)-\left(1+2+2^2+...+2^{2017}\right)$

$\Rightarrow A=2^{2018}-1\left(đpcm\right)$

Câu trả lời:

$A=1+2+2^2+2^3+...+2^{2017}$

$\Rightarrow2A=2+2^2+2^3+2^4+...+2^{2018}$

$\Rightarrow2A-A=\left(2+2^2+2^3+...+2^{2018}\right)-\left(1+2+2^2+...+2^{2017}\right)$

$\Rightarrow A=2^{2018}-1\left(đpcm\right)$

Nguyễn Hữu Triết · Answer

$A=1+2+2^2+2^3+...+2^{2017}$

$\Rightarrow2A=2+2^2+2^3+2^4+...+2^{2018}$

$\Rightarrow2A-A=\left(2+2^2+2^3+...+2^{2018}\right)$$-\left(1+2+2^2+...+2^{2017}\right)$

$\Rightarrow A=2^{2018}-1$

Câu trả lời:

$A=1+2+2^2+2^3+...+2^{2017}$

$\Rightarrow2A=2+2^2+2^3+2^4+...+2^{2018}$

$\Rightarrow2A-A=\left(2+2^2+2^3+...+2^{2018}\right)$$-\left(1+2+2^2+...+2^{2017}\right)$

$\Rightarrow A=2^{2018}-1$