Question

Cho C =  1 + 3 + 3 mũ 2 + 3 mũ 3 + .... + 3 mũ 11 .Chứng  tỏ rằng C chia hết cho 4

 

Answer 1

\(C=1+3+3^2+3^3+...+3^{11}\)

\(C=\left(1+3\right)+\left(3^2+3^3\right)+...+\left(3^{10}+3^{11}\right)\)

\(C=4+3^2.\left(1+3\right)+...+3^{10}.\left(1+3\right)\)

\(C=4+3^2.4+...+3^{10}.4\)

\(C=4.\left(1+3^2+...+3^{10}\right)\)

Vif \(4⋮4=>C⋮4\)

Answer 2

\(C=1+3+3^2+3^3+...+3^{11}\\ =\left(1+3\right)+3^2\left(1+3\right)+...+3^{10}\left(1+3\right)\\ =\left(1+3\right)\left(1+3^2+....+3^{10}\right)\\ =4\left(1+3^2+....+3^{10}\right)⋮4\)

\(=>C⋮4\)

Answer 3

C=1+3+32+33+...+311C=1+3+32+33+...+311

C=(1+3)+(32+33)+...+(310+311)C=(1+3)+(32+33)+...+(310+311)

C=4+32.(1+3)+...+310.(1+3)C=4+32.(1+3)+...+310.(1+3)

C=4+32.4+...+310.4C=4+32.4+...+310.4

C=4.(1+32+...+310)C=4.(1+32+...+310)

Vif 4⋮4=>C⋮4