+)Ta có:\(A=2019+2019^2+2019^3+2019^4+2019^5+2019^6\)
\(\Rightarrow A=\left(2019+2019^2\right)+\left(2019^3+2019^4\right)+\left(2019^5+2019^6\right)\)
\(\Rightarrow A=\left(2019+2019^2\right)+2019^2.\left(2019+2019^2\right)+2019^4.\left(2019+2019^2\right)\)
+)Ta lại có:20192 tận cùng là 1
=>2019+20192 tân cùng là 9+1=10
=>2019+20192\(⋮2\)
\(\Rightarrow\left(2019+2019^2\right)⋮2;2019^2.\left(2019+2019^2\right)⋮2;2019^4.\left(2019+2019^2\right)⋮2\)
\(\Rightarrow A⋮2\)
Vậy \(A⋮2\left(ĐPCM\right)\)
Chúc bn học tốt
A = 2019 + 20192 + 20193 + 20194 + 20195 + 20196
A = ( 2019 + 20192 ) + ( 20193 + 20194) + ( 20195 + 20196)
A = 1 . ( 2019 + 20192 ) + 20193 . (2019 + 20192 ) + 20195 . ( 2019 + 20192 )
A = 1 . 4 078 380 + 20193 . 4 078 380 + 20195 . 4 078 380
A = 4 078 380 . ( 1 + 20193 + 20195) \(⋮2\rightarrowĐPCM\)
# HOK TỐT #
\(A=2019+2019^2+2019^3+2019^4+2019^5+2019^6\)
<=> \(A=\left(2019+2019^2\right)+\left(2019^3+2019^4\right)+\left(2019^5+2019^6\right)\)
<=>\(A=2019.\left(1+2019\right)+2019^3.\left(1+2019\right)+2019^5\left(1+2019\right)\)
<=>\(A=2019.2020+2019^3.2020+2019^5.2020\)
<=>\(A=2020.\left(2019+2019^3+2019^5\right)\)
<=>\(A=2.1010\left(2019+2019^3+2019^5\right)⋮2\)=> \(A⋮2\)
Vậy .....