Question

Chứng minh: 2+2²+2³+2⁴+...........+2²⁰¹⁵ chia hết cho 3

Answer 1

    2+2^2+2^3+2^4+........+2^2015

= (2+2^2+2^3+2^4)+ (2^5+2^6+2^7+2^8)+......+(2^2012+2^2013+2^2014+2^2015)

= 2.(1+2+2^2+2^3) + 2^5. (1+2+2^2+2^3) + .....+ 2^2012.(1+2+2^2+2^3)

= 2.15 + 2^5.15 +.....+ 2^2012.15

= (2+2^5+....+2^2012).15 chia hết cho 3(do 15 chia hết cho 3)