Question

chứng tỏ rằng A= 2+ 2^2 + 2^3 + .... + 2^2016 chia hết cho 3;7;15

Answer 1

`A = 2(1 + 2) + 2^2(1 + 2) + ... + 2^2015(1+2) = 3 (2 + 2^2 + ... + 2^2015) vdots 3.`

`A = 1(2+2^2+2^3) + 2^3(2+2^2 + 2^3) + ... + 2^2013(2 + 2^2 + 2^3)`

`= 14 . (1+2^3 + ... + 2^2013) vdots 7`.

`A = 1 .(2+2^2+2^3+2^4) + 2^4(2+2^2+2^3+2^4) + ... + 2^2012(2 + 2^2 + 2^3 + 2^4)`

`= 30 . (1 + 2^4 + ... + 2^2012) vdots 15`.