Question

So sánh A =  \(\dfrac{10^{2021}+1}{10^{2022}+1}\) và B = \(\dfrac{10^{2022}+1}{10^{2023}+1}\)

Answer 1

Ta có:

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

`10A = (10 .(10^2021 +1))/(10^2022 + 1)`

`10A  = (10^2022 + 10)/(10^2022 + 1)`

`10A = 1+9/(10^2022 + 1)`

Ta có:

`B = (10^2022 + 1)/(10^2023 + 1)`

`10B = (10. (10^2022 + 1))/(10^2023 + 1)`

`10B =(10^2023 + 10)/(10^2023 + 1)`

`10B = 1 + 9/(10^2023 + 1)`

Vì: `9/(10^2022 + 1)>9/(10^2023 + 1)` nên `A>B`

Vậy: `A>B`