Câu hỏi của Nguyễn Duy Khang

Question

Số dư của $A=2^0+2^1+2^2+...+2^{2012}$ khi chia cho 7 là???

Thu · Accepted Answer

$A=\left(2^0+2^1+2^2\right)+\left(2^3+2^4+2^5\right)+....+\left(2^{2010}+2^{2011}+2^{2012}\right)$

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

$A=7+7.2^3+....+7.2^{2010}$

$A=7.\left(1+2^3+2^{2010}\right)$ chia hết cho 7.

Vậy A chia 7 dư 0

Câu trả lời:

$A=\left(2^0+2^1+2^2\right)+\left(2^3+2^4+2^5\right)+....+\left(2^{2010}+2^{2011}+2^{2012}\right)$

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

$A=7+7.2^3+....+7.2^{2010}$

$A=7.\left(1+2^3+2^{2010}\right)$ chia hết cho 7.

Vậy A chia 7 dư 0