Question

tìm số dư trong tổng sau:  2^0+2^1+2^2+....+2^2014: 7

Answer 1

\(2^0+2^1+2^2+2^3+...+2^{2014}.\)

\(=1+\left(2^1+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+.....+\left(2^{2012}+2^{2013}+2^{2014}\right)\)

\(=1+2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+....+2^{2012}\left(1+2+2^2\right)\)

\(=1+2.7+2^4.7+.....+2^{2012}.7\)

\(=1+7\left(2+2^4+....+2^{2012}\right)\)

\(7\left(2+2^4+...+2^{2012}\right)⋮7\)\(\Rightarrow\)\(2^0+2^1+2^2+2^3+...+2^{2014}\)\(chia7\)\(dư1\)