a/ \(A=3+3^2+3^3+3^4+.............+3^{49}+3^{50}\)
\(=\left(3+3^2\right)+\left(3^3+3^4\right)+............+\left(3^{49}+3^{50}\right)\)
\(=3\left(1+3\right)+3^3\left(1+3\right)+............+3^{49}\left(1+3\right)\)
\(=3.4+3^3.4+...............+3^{49}.4\)
\(=4\left(3+3^3+...........+3^{49}\right)⋮4\)
\(\Leftrightarrow A⋮4\left(đpcm\right)\)
b/ \(A=3+3^2+3^3+3^4+.............+3^{49}+3^{50}\)
\(=\left(3+3^2+3^3+3^4\right)+\left(3^5+3^6+3^7+3^9\right)+........+\left(+3^{47}+3^{48}+3^{49}+3^{50}\right)\)
\(=3\left(1+3+3^2+3^3\right)+3^5\left(1+3+3^2+3^3\right)+........+3^{47}\left(1+3+3^2+3^3\right)\)
\(=3.40+3^5.40+.........+3^{47}.40\)
\(=40\left(3+3^5+...........+3^{47}\right)⋮10\)
\(\Leftrightarrow A⋮10\left(đpcm\right)\)
