Question

Chứng tỏ rằng B=1+2+2^2+...+2^2020 chia hết cho 7

Answer 1

\(B=1+2+2^{2}(1+2+2^{2})+2^{5}(1+2+2^{2})+...+2^{2018}(1+2+2^{2})\)

    \(=3+(1+2+2^{2})(2^{2}+2^{5}+2^{8}+...+2^{2018})\)

    \(=3+ 7.(2^{2}+2^{5}+2^{8}+...+2^{2018})\), không chia hết cho 7.