Câu hỏi của Minh Hà

Question

P/S:bai nay khong lien quan den uoc va boi

2 mũ 1 +...+2 mũ 10 co chia het cho 3 khong

may ban than dong giup minh voi

Nguyễn Đắc Nhật · Accepted Answer

21+22+23+......+210

⇒2.(1+2)+22.(1+2)+......+29.(1+2)

⇒2.3+22.3+........+29.3

⇒3.(2+22+....+29)⋮3

Vậy 21+22+23+....+210⋮3 (đpcm)Câu trả lời: 21+22+23+......+210

⇒2.(1+2)+22.(1+2)+......+29.(1+2)

⇒2.3+22.3+........+29.3

⇒3.(2+22+....+29)⋮3

Vậy 21+22+23+....+210⋮3 (đpcm)

Sakuraba Laura · Answer

Đặt biểu thức trên là A, ta có:

$A=2^1+2^2+2^3+...+2^{10}$

$A=\left(2^1+2^2\right)+\left(2^3+2^4\right)+...+\left(2^9+2^{10}\right)$

$A=2^1.\left(1+2\right)+2^3.\left(1+2\right)+...+2^9.\left(1+2\right)$

$A=2^1.3+2^3.3+...+2^9.3$

$A=3.\left(2^1+2^3+...+2^9\right)$

$\Rightarrow A⋮3$Câu trả lời: Đặt biểu thức trên là A, ta có:

$A=2^1+2^2+2^3+...+2^{10}$

$A=\left(2^1+2^2\right)+\left(2^3+2^4\right)+...+\left(2^9+2^{10}\right)$

$A=2^1.\left(1+2\right)+2^3.\left(1+2\right)+...+2^9.\left(1+2\right)$

$A=2^1.3+2^3.3+...+2^9.3$

$A=3.\left(2^1+2^3+...+2^9\right)$

$\Rightarrow A⋮3$