Câu hỏi của Nguyen

Question

Cho : P=$2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^{10}$

Chứng minh P chia hết cho 31

Mashiro Shiina · Accepted Answer

$P=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^{10}$

$P=2\left[\left(1+2+2^2+2^3+2^4\right)+\left(2^5+2^6+2^7+2^8+2^9\right)\right]$

$P=2\left[\left(1+2+2^2+2^3+2^4\right)+2^5\left(1+2+2^2+2^3+2^4\right)\right]$

$P=2\left(2^5+1\right)\left(1+2+2^2+2^3+2^4\right)$

Mà: $1+2+2^2+2^3+2^4=31\Rightarrow P⋮31\left(đpcm\right)$Câu trả lời: $P=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^{10}$

$P=2\left[\left(1+2+2^2+2^3+2^4\right)+\left(2^5+2^6+2^7+2^8+2^9\right)\right]$

$P=2\left[\left(1+2+2^2+2^3+2^4\right)+2^5\left(1+2+2^2+2^3+2^4\right)\right]$

$P=2\left(2^5+1\right)\left(1+2+2^2+2^3+2^4\right)$

Mà: $1+2+2^2+2^3+2^4=31\Rightarrow P⋮31\left(đpcm\right)$

Chương III : Phân số