\(\dfrac{2022\times2023-1}{2023\times2021+2022}\)

= \(\dfrac{\left(2021+1\right)\times2023-1}{2023\times2021+2022}\)

= \(\dfrac{2023\times2021+2023-1}{2023\times2021+2022}\)

= \(\dfrac{2023\times2021+2022}{2023\times2021+2022}\)

= 1

$\genfrac{}{}{0ex}{}{2022\times 2023-1}{2023\times 2021+2022}$

= $\genfrac{}{}{0ex}{}{\left(2021+1\right)\times 2023-1}{2023\times 2021+2022}$

= $\genfrac{}{}{0ex}{}{2023\times 2021+2023-1}{2023\times 2021+2022}$

= $\genfrac{}{}{0ex}{}{2023\times 2021+2022}{2023\times 2021+2022}$

= 1

a: \(B=\dfrac{154}{155+156}+\dfrac{155}{155+156}\)

\(\dfrac{154}{155}>\dfrac{154}{155+156}\)

\(\dfrac{155}{156}>\dfrac{155}{155+156}\)

=>154/155+155/156>(154+155)/(155+156)

=>A>B

b: \(C=\dfrac{2021+2022+2023}{2022+2023+2024}=\dfrac{2021}{6069}+\dfrac{2022}{6069}+\dfrac{2023}{6069}\)

2021/2022>2021/6069

2022/2023>2022/2069

2023/2024>2023/6069

=>D>C

Ta có: C = 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + ... + 1/2021.2022.2023

=> C = 1/2. (3-1/1.2.3 + 4-2/2.3.4 + 5-3/3.4.5 + ... + 2023-2021/2021.2022.2023

=> C = 1/2. (1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + 1/3.4 - 1/4.5 + ... + 1/2021.2022 - 1/2022.2023)

=> C = 1/2. (1/1.2 - 1/2022.2023)

- Phần còn lại bạn tự tính chứ số to quá

2023/2022=1+1/2022

2022/2021=1+1/2021

mà 2022>2021

nên 2023/2022<2022/2021

2022x(2023-155)-2023x(2022-155)

=2022x2023-2022x155-2023x2022+2023x155

=(2022x2023-2023x2022)+(2023x155-2022x155)

=0+155x(2023-2022)

=155x1=155

kết quả là 1022 nhé bạn