Question

c/m rằng A = 7^1+7^2+7^3+7^4+....+7^4k (k thuộc Z) chia hết cho 400 .

Mn ơi giúp mk vs nha , cần giải gấp

Answer 1

\(A=7+7^2+7^3+..........+7^{4n}\)

\(\Leftrightarrow A=\left(7+7^2+7^3+7^4\right)+..........+\left(7^{4n-3}+7^{4n-2}+7^{4n-1}+7^{4n}\right)\)

\(\Leftrightarrow A=7\left(1+7+7^2+7^3\right)+.........+7^{4n-3}\left(1+7+7^2+7^3\right)\)

\(\Leftrightarrow A=7.400+7^5.400+..........+7^{4n-3}.400\)

\(\Leftrightarrow A=400\left(7+7^5+........+7^{4n-3}\right)⋮400\)

\(\Leftrightarrow A⋮400\rightarrowđpcm\)

Answer 2

\(A=7^1+7^2+7^3+7^4+7^{4k}\)

=\(7\left(1+7^1+7^2+7^3\right)+...+7^{4k-3}\left(1+7^1+7^2+7^3\right)\)

=\(400\left(7+...+7^{4k-3}\right)⋮400\)

Do đó:\(A⋮400\left(đpcm\right)\)