Question

Chứng tỏ rằng: (2\(^{10}\) \(+\)2\(^{11}\) \(+\) 2\(^{12}\) )\(⋮\) 7

Answer 1

Đặt:

\(A=\left(2^{10}+2^{11}+2^{12}\right)\)

\(A=\left(2^{10}+2^{10}.2+2^{10}.2^2\right)\)

\(A=2^{10}\left(2+2^2+1\right)\)

\(A=2^{10}.7\)

\(\Leftrightarrow A⋮7\)

Answer 2

\(2^{10}+2^{11}+2^{12}=2^{10}\left(1+2+2^2\right)=2^{10}.7⋮7\)

\(\Rightarrowđpcm\)

Answer 3

Ta có: 2¹⁰+2¹¹+2¹²=2¹⁰+2¹⁰.2+2¹⁰.2²=2¹⁰.(1+2+2²)=2¹⁰.7\(⋮\)7

=>2¹⁰+2¹¹+2¹²\(⋮\)7(ĐPCM)

Answer 4

Ta có:

\(2^{10}+2^{11}+2^{12}=2^{10}.1+2^{10}.2+2^{10}.2^2=2^{10}.\left(1+2+2^2\right)=2^{10}.7\) chia hết cho 7

=>\(2^{10}+2^{11}+2^{12}\) chia hết cho 7