Question

Cho S=1+4+4²+4³+4⁴+4⁵+...+4⁹⁸+4⁹⁹. Chứng tỏ rằng s chia hết cho 5

Giúp mk với!! Cảm ơn rất nhiều!!!

Answer 1

\(S=\left(1+4\right)+\left(4^2+4^3\right)+...+\left(4^{98}+4^{99}\right)\\ S=\left(1+4\right)+4^2\left(1+4\right)+...+4^{98}\left(1+4\right)\\ S=\left(1+4\right)\left(1+4^2+...+4^{98}\right)=5\left(1+4^2+...+4^{98}\right)⋮5\)

Answer 2

\(S=\left(1+4\right)+...+4^{98}\left(1+4\right)\)

\(=5\left(1+...+4^{98}\right)⋮5\)