Đặt:
\(A=1+3+3^2+3^3+.....+3^{11}\)
\(A=\left(1+3\right)+\left(3^2+3^3\right)+.....+\left(3^{10}+3^{11}\right)\)
\(A=1\left(1+3\right)+3^2\left(1+3\right)+.....+3^{10}\left(1+3\right)\)
\(A=1.4+3^2.4+....+3^{10}.4\)
\(A=4\left(1+3^2+...+3^{10}\right)\)
\(A⋮4\rightarrowđpcm\)
Đặt : B = 1 + 3 + 32 + 33 + ........+311
B = (1+3 ) +(32+33)+..........+ (310+311)
B=1.(1+3)+32.(1+3 ) +............+ 310 . ( 1+3)
B = 1.4 + 32.4 +.................+ 310.4
B = 4.(1+32+..............+310)
Mà 4 \(⋮\) 4
=>4.(1+32+.........+310) \(⋮\)4
Vậy B \(⋮\)4
