Đặt \(A=5+5^2+5^3+...+5^{100}\)
\(=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{99}+5^{100}\right)\)
\(=5\left(1+5\right)+5^3\left(1+5\right)+...+5^{99}\left(1+5\right)\)
\(=5.6+5^3.6+...+5^{99}.6\)
\(=\left(5+5^3+...+5^{99}\right).6⋮6\)
\(\Rightarrow\) \(A⋮6\)
\(A=5+5^2+5^3+...+5^{100}\)
\(A=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{99}+5^{100}\right)\)
\(A=5\left(1+5\right)+5^3\left(1+5\right)+...+5^{99}\left(1+5\right)\)
\(A=5\cdot6+5^3\cdot6+...+5^{99}\cdot6\)
\(A=6\cdot\left(5+5^3+5^5+...+5^{99}\right)\)
\(\Rightarrow\)\(A\)chia hết cho 6
