Question

chứng tỏ rằng:2+2^2+2^3+....+2^2016chia hết cho 3

Answer 1

2+2²+2³+....+2²⁰¹⁶ =(2+2²)+ (2³+2⁴ )+....+(2²⁰¹⁵ +2²⁰¹⁶)

=2*(1+2)+.....+2²⁰¹⁵ *(1+2)

=2*3+.......+2²⁰¹⁵*3

=3(2+.......+2²⁰¹⁵) chia hết cho 3

Answer 2

2 + 2^2 +2^3 + ......  +2^2016

= (2+2^2) + ..  +(2^2015 + 2^2016)

= 2.3 + .. + 2^2015.3

= 3.(2+2^3+...+2^2015)

Chia hết cho 3 

Answer 3

(2+2²)+(2³+2⁴)+....+(2²⁰¹⁵+2²⁰¹⁶)

(2.1+2.2)+(2³.1+2³.2)+....+(2²⁰¹⁵.1+2²⁰¹⁵.2)

2(1+2)+2³(1+3)+...+2²⁰¹⁵(1+2)

2.3+2³.3+...+2²⁰¹⁵.3

3(2+2³+...2²⁰¹⁵)

Vì 3 chia hết cho 3=>3(2+23+...+22015​) chia hết cho 3 hay 2+22+23+....+22016 chia hết c​ho 3