\(A=5+5^2+5^3+...+5^{30}.\)
\(A=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{29}+5^{30}\right).\)
\(A=5\left(1+5\right)+5^3\left(1+5\right)+...+5^{29}\left(1+5\right).\)
\(A=5.6+5^3.6+...+5^{29}.6.\)
\(A=6\left(5+5^3+...+5^{29}\right)⋮6\left(đpcm\right).\)