Question

A=2+2\(^2\)+2\(^3\)+2\(^4\)+........+2\(^{2020}\) chứng minh rằng phép tình này chia hết cho 3

 

 

 

Answer 1

\(A=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{2019}\left(1+2\right)\\ A=3\left(2+2^3+...+2^{2019}\right)⋮3\)

Answer 2

\(A=2+2^2+2^3+...+2^{2020}\)

\(=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{2019}\left(1+2\right)\)

\(=2.3+2^3.3+...+2^{2019}.3\)

\(=3\left(2+2^3+...+2^{2019}\right)⋮3\)

Answer 3

\(A=2\cdot\left(1+2\right)+...+2^{2019}\left(1+2\right)\)

\(=3\cdot\left(2+...+2^{2019}\right)⋮3\)