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\(2022A=2022+2022^2+2022^3+2022^4+...+2022^{2018}\)
\(2021A=2022A-A=2022^{2018}-1\Rightarrow A=\dfrac{2022^{2018}-1}{2021}\)
\(\Rightarrow A< B\)
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Ta có:
\(2023^{2022}=2023\cdot2023^{2021}\)
\(2022^{2022}+2022^{2021}=2022^{2021}\cdot\left(2022+1\right)=2023\cdot2022^{2021}\)
Mà: \(2023>2022\)
\(\Rightarrow2023^{2021}>2022^{2021}\)
\(\Rightarrow2023^{2021}\cdot2023>2022^{2021}\cdot2023\)
\(\Rightarrow2023^{2022}>2022^{2022}+2022^{2021}\)
Vậy: ...
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Tính nhanh: A= \(\dfrac{2022}{1.2}+\dfrac{2022}{2.3}+\dfrac{2022}{3.4}+...+\dfrac{2022}{2021.2022}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A=2022(1/1-1/2+1/2-1/3+...+1/2021-1/2022)
=2022(1/1-1/2022)
=2022.2021/2022
ket qua tu tinh nha
A = \(\dfrac{2022}{1.2}+\dfrac{2022}{2.3}+\dfrac{2022}{3.4}+...+\dfrac{2022}{2021.2022}\)
= \(\dfrac{2022}{1}-\dfrac{2022}{2}+\dfrac{2022}{2}-\dfrac{2022}{3}+\dfrac{2022}{3}-\dfrac{2022}{4}+...+\dfrac{2022}{2021}-\dfrac{2022}{2022}\)
= \(\dfrac{2022}{1}-\dfrac{2022}{2022}\)
= \(2021\)
Chúc bạn học tốt!! ^^
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\(\dfrac{1}{2022}\cdot A=\dfrac{2022^{100}+1}{2022^{100}+100}=1-\dfrac{99}{2022^{100}+100}\)
\(\dfrac{1}{2022}B=\dfrac{2022^{101}+1}{2022^{101}+100}=1-\dfrac{9}{2022^{101}+100}\)
2022^100+100<2022^101+100
=>-99/2022^100+100<-99/2022^101+100
=>A<B
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Ta có tính chất: \(\dfrac{a}{b}>\dfrac{a-m}{b-m}\)
\(A=\dfrac{2022^{99}-1}{2022^{100}-1}>\dfrac{2022^{99}-1-2021}{2022^{100}-1-2021}\)
\(A>\dfrac{2022^{99}-2022}{2022^{100}-2022}\)
\(A>\dfrac{2022\left(2022^{98}-1\right)}{2022\left(2022^{99}-1\right)}\)
\(A>\dfrac{2022^{98}-1}{2022^{99}-1}\)
\(A>B\)
2022+2022x247+752-2022
=2022(1+247+752)
=2022x1000
=2022000
500186