`7)`
- Ta có :
`A = 2018.2018`
`A = 2018(2020 - 2)`
`A = 2018.2020 - 2018.2`
`B = 2016.2020`
`B = 2020(2018 - 2)`
`B = 2020.2018 - 2020.2`
- Vì `2018.2 < 2020.2 => 2018.2020-2018.2 > 2020.2018-2020.2`
`=> A > B`
`8)`
`a)` - Ta có :
`A = 2 + 2^2 + 2^3 + 2^4 + ... + 2^11 + 2^12`
`A = (2 + 2^2) + (2^3 + 2^4) + ... + (2^11 + 2^12)`
`A = 6 + 2^2 (2 + 2^2) + ... + 2^10 (2 + 2^2)`
`A = 6 + 2^2 .6 + ... + 2^10 .6`
`A = 6(1 + 2^2 + ... + 2^10)`
- Ta lại có : `6 vdots 6`
`=> 6(1 + 2^2 + ... + 2^10) vdots 6`
`=> A vdots 6`
`b)` - Ta có :
`A = 2 + 2^2 + 2^3 + 2^4 + ... + 2^11 + 2^12`
`A = (2 + 2^2 + 2^3) + (2^4 + 2^5 + 2^6) + ... + (2^10 + 2^11 + 2^12)`
`A = 14 + 2^3 (2 + 2^2+2^3) + ... + 2^9 (2 + 2^2+2^3)`
`A = 14 + 2^3 .14 + ... + 2^9 .14`
`A = 14(1 + 2^3 + ... + 2^9)`
- Ta lại có : `14 vdots 7`
`=> 14(1 + 2^3 + ... + 2^9) vdots 7`
`=> A vdots 7`