Question

chứng minh rằng;

(7^{0 +} 7^{1 +} 7²⁺ 7^{3 +  . . . . . . . . . . . .  +} 7²⁰¹⁰ + 72011 ) chia hết cho 8

Answer 1

=(1+7) + 7².1 + 7².7+.............................+7²⁰¹⁰.(7+1)

=8+7².(1+7)+..............................+7²⁰¹⁰.(1+7)

=8.1+7².8+..................................+7²⁰¹⁰.8

=8.(1+7²+7⁴+7⁶+....................+7²⁰¹⁰) chia hết cho 8

Answer 2

(7^0+7^1+7^2+7^3+...+7^2010+7^2011):8   

=(7^0+7^1)+(7^2+7^30+...+(7^2010+7^2011) 

=(7^0.7^0+7^1.7^0)+...+(7^2010.7^0+7^2011.7^1) 

=7^0+7^0+...+7^0  <p>

=7^0:8</p>

Answer 3

\(\text{(7^0+7^1+7^2+7^3+...+7^2010+7^2011):8}\)

\(\text{=(7^0+7^1)+(7^2+7^30+...+(7^2010+7^2011)}\)

\(\text{=(7^0.7^0+7^1.7^0)+...+(7^2010.7^0+7^2011.7^1)}\)

\(\text{=7^0+7^0+...+7^0}\)

\(\text{=7^0:8}\)