Question

 

Answer 1

`A = (10^2020 + 1)/(10^2021 + 1) < (10^2020 + 1 + 9)/(10^2021 + 1 + 9)`

`= (10^2020 + 10)/(10^2021 + 10)`

`= (10^2021)/(10^2022) < (10^2021+1)/(10^2022 + 1)`

`=> A < B`.

Answer 2

`10A = (10^2021 + 10)/(10^2021 + 1) = (20^2021 + 1 + 9)/(10^2021 + 1) = (10^2021 + 1)/(10^2021 + 1) + 9/(10^2021 + 1)=1 + 9/(10^2021 + 1) `

`10B =  (10^2022 + 10)/(10^2022 + 1) = (20^2022 + 1 + 9)/(10^2022 + 1) = (10^2022 + 1)/(10^2022 + 1) + 9/(10^2022 + 1) = 1 + 9/(10^2022+1)`

Vì `9^(10^2021 + 1) > 9^(10^2022+1)`

`=> 1 + 9^(10^2021 + 1) < 1+9^(10^2022+1)`

`=> A<B`

Vậy `A<B`

Answer 3

`\text{Câu 5:}`

Ta có :

`+A={10^2020+1}/{10^2021+1}`

`->10A={10(10^2020+1)}/{10^2021+1}`

`->10A={10^2021+10}/{10^2021+1}`

`->10A={10^2021+1+9}/{10^2021+1}`

`->10A=1+9/{10^2021+1}`

\(+B=\dfrac{10^{2021}+1}{10^{2022}+1}\)

\(10B=\dfrac{10\left(10^{2021}+1\right)}{10^{2022}+1}\)

\(10B=\dfrac{10^{2022}+10}{10^{2022}+1}\)

\(10B=\dfrac{10^{2022}+1+9}{10^{2022}+1}\)

\(10B=1+\dfrac{9}{10^{2022}+1}\)

`A>B`