Question

Chứng minh: \(1+5+5^2+5^3+...+5^{99}\) chia hết cho 6

Answer 1

\(1+5+5^2+5^3+...+5^{99}\)

\(=\left(1+5\right)+5^2\left(1+5\right)+...+5^{98}\left(1+5\right)\)

\(=6+5^2.6+...+5^{98}.6\)

\(=6\left(1+5^2+...+5^{98}\right)⋮6\)