`a)`Ta có:
`B=[2019+2020+2021]/[2020+2021+2022]=2019/[2020+2021+2022]+2020/[2020+2021+2022]+2022/[2020+2021+2022]`
Vì:
`2019/[2020+2021+2022]<2019/2020(1)`
`2020/[2020+2021+2022]<2020/2021(2)`
`2021/[2020+2021+2022]<2021/2022(3)`
Từ `(1),(2),(3)=>B<A`
Vậy `B<A`
`b)`Đặt:
`C=[7^2018+1]/5^2018;D=[5^2018+1]/5^2017`
Theo bài ra ta có:
`D=[5(5^2018+1)]/[5^2017. 5]`
Do `C,D` có cùng mẫu,nên ta đi so sánh tử:
`C=7^2018+1;D=[5(5^2018+1)]`
Ta có:
`7^2018<5.5^2018`
`1<5.1`
`=>C<D`
$#Rabifoot$