Đề sai, tớ sửa lại
Ta có :
\(A=2+2^2+..............+2^{60}\)
\(\Leftrightarrow A=\left(2+2^2\right)+\left(2^3+2^4\right)+...........+\left(2^{59}+2^{60}\right)\)
\(\Leftrightarrow A=2\left(1+2\right)+2^3\left(1+2\right)+.........+2^{59}\left(1+2\right)\)
\(\Leftrightarrow A=2.3+2^3.3+...........+2^{59}.3\)
\(\Leftrightarrow A=3\left(2+2^2+..........+2^{59}\right)\)
\(\Leftrightarrow A⋮3\rightarrowđpcm\)
Lại có :
\(A=2+2^2+2^3+............+2^{60}\)
\(\Leftrightarrow A=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+..........+\left(2^{58}+2^{59}+2^{60}\right)\)
\(\Leftrightarrow A=2\left(1+2+2^2\right)+2^3\left(1+2+2^2\right)+..........+2^{59}\left(1+2+2^2\right)\)
\(\Leftrightarrow A=2.7+2^4.7+............+2^{58}.7\)
\(\Leftrightarrow A=7\left(2+2^3+..........+2^{58}\right)\)
\(\Leftrightarrow A⋮7\rightarrowđpcm\)
Ta tiếp tục có :
\(A=2+2^2+2^3+............+2^{60}\)
\(\Leftrightarrow A=\left(2+2^2+2^3+2^4\right)+..............+\left(2^{57}+2^{58}+2^{59}+2^{60}\right)\)
\(\Leftrightarrow A=2\left(1+2+2^2+2^3\right)+.............+2^{57}\left(1+2+2^2+2^3\right)\)
\(\Leftrightarrow A=2.15+............+2^{57}.15\)
\(\Leftrightarrow A=15\left(2+.........+2^{57}\right)\)
\(\Leftrightarrow A⋮15\rightarrowđpcm\)
