Question

BT3 :Chứng Minh

6) S = 2 + 2\(^2\) + 2\(^3\) + .... + 2\(^{12}\) chia hết cho 3 , chia hết cho 7 ; 5 ; 6

Answer 1

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

\(=3\left(2+2^3+...+2^{11}\right)⋮3\)

\(S=2\left(1+2+2^2\right)+...+2^{10}\left(1+2+2^2\right)\)

\(=7\cdot\left(2+...+2^{10}\right)⋮7\)

\(S=3\left(2+2^3+...+2^{11}\right)=3\cdot2\left(1+2^2+...+2^{10}\right)=6\left(1+2^2+...+2^{10}\right)⋮6\)