Question

2+2^2+2^3+...................+2^56 chia hết cho 5

Answer 1

\(2+2^2+2^3+...+2^{56}\\ =\left(2+2^2+2^3+2^4\right)+2^4\left(2+2^2+2^3+2^4\right)+...+2^{52}\left(2+2^2+2^3+2^4\right)\\ =30+2^4.30+...+2^{52}.30\\ =30.\left(1+2^4+...+2^{52}\right)=5.6.\left(1+2^4+...+2^{52}\right)⋮5\left(ĐPCM\right)\)