Câu hỏi của LÊ TRẦN BÁCH

Question

S=2⁰ + 2¹ + 2² +...+ 2⁷

chứng tỏ S chia cho 3

Nguyễn Đức Trí · Accepted Answer

$S=2^0+2^1+2^2+...+2^7$

$\Rightarrow S=\left(2^0+2^1\right)+2^2\left(2^0+2^1\right)+...+2^6\left(2^0+2^1\right)$

$\Rightarrow S=3+2^2.3+...+2^6.3$

$\Rightarrow S=3\left(1+2^2+...+2^6\right)⋮3$

$\Rightarrow dpcm$

Câu trả lời:

$S=2^0+2^1+2^2+...+2^7$

$\Rightarrow S=\left(2^0+2^1\right)+2^2\left(2^0+2^1\right)+...+2^6\left(2^0+2^1\right)$

$\Rightarrow S=3+2^2.3+...+2^6.3$

$\Rightarrow S=3\left(1+2^2+...+2^6\right)⋮3$

$\Rightarrow dpcm$