\(A=7+7^2+7^3+...+7^8\\=(7+7^2)+(7^3+7^4)+...+(7^7+7^8)\\=7\cdot(1+7)+7^3\cdot(1+7)+...+7^7\cdot(1+7)\\=7\cdot8+7^3\cdot8+...+7^7\cdot8\\=8\cdot(7+7^3+...+7^7)\)
Vì \(8\cdot(7+7^3+...+7^7)\vdots8\)
nên \(A\vdots8\)
\(A=7+7^2+7^3+...+7^8\)
\(A=\left(7+7^2\right)+\left(7^3+7^4\right)+...+\left(7^7+7^8\right)\)
\(A=56+7^2.\left(7+7^2\right)+...+7^6.\left(7+7^2\right)\)
\(A=56+7^2.56+...+7^6.56\)
\(A=56.\left(1+7^2+...+7^6\right)\)
Vì \(56⋮8\) nên \(56.\left(1+7^2+...+7^6\right)⋮8\)
Vậy \(A⋮8\)
\(#WendyDang\)