Question

[Jeon Jungkook]

CHONG MINH RẰNG:

2²+2³+2⁴⁺.......+2^{2017  chia hết cho 21}

^{giúp vỡi♥♥♥}

Answer 1

[Phạm Tuấn Đạt]

\(2^2+2^3+2^4+...+2^{2017}\)

\(=\left(2^2+2^3+2^4+2^5+2^6+2^7\right)+...+\left(2^{2012}+2^{2013}+...+2^{2017}\right)\)

\(=2^2\left(1+2+2^2+...+2^5\right)+....+2^{2012}\left(1+2+...+2^5\right)\)

\(=63\left(2^2+...+2^{2012}\right)⋮21\)