So sánh
A = \(\dfrac{2022^{2023}+1}{2022^{2024}+1}\) và B = \(\dfrac{2022^{2022}+1}{2022^{2023}+1}\)
Những câu hỏi liên quan
A=\(\dfrac{2022^{2022}+1}{2022^{2023}+1}\) ; B= \(\dfrac{2022^{2023}+1}{2022^{2024}+1}\) So sánh A và B
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13 tháng 2 2023 lúc 22:28
Giúp mình với!!!
So sánh A=\(\dfrac{2024^{2023}+1}{2024^{2024}+1}\) và B=\(\dfrac{2024^{2022}+1}{2024^{2023}+1}\)
Cám ơn các bạn!
\(A=\dfrac{2024^{2023}+1}{2024^{2024}+1}\)
\(2024A=\dfrac{2024^{2024}+2024}{2024^{2024}+1}=\dfrac{\left(2024^{2024}+1\right)+2023}{2024^{2024}+1}=\dfrac{2024^{2024}+1}{2024^{2024}+1}+\dfrac{2023}{2024^{2024}+1}=1+\dfrac{2023}{2024^{2024}+1}\)
\(B=\dfrac{2024^{2022}+1}{2024^{2023}+1}\)
\(2024B=\dfrac{2024^{2023}+2024}{2024^{2023}+1}=\dfrac{\left(2024^{2023}+1\right)+2023}{2024^{2023}+1}=\dfrac{2024^{2023}+1}{2024^{2023}+1}+\dfrac{2023}{2024^{2023}+1}=1+\dfrac{2023}{2024^{2023}+1}\)
Vì \(2024>2023=>2024^{2024}>2024^{2023}\)
\(=>2024^{2024}+1>2024^{2023}+1\)
\(=>\dfrac{2023}{2024^{2023}+1}>\dfrac{2023}{2024^{2024}+1}\)
\(=>A< B\)
\(#PaooNqoccc\)
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2 tháng 5 2022 lúc 11:47
So sánh 2 phân số
A = \(\dfrac{2022^{2022}+1}{2022^{2021}+1}\) ; B = \(\dfrac{2022^{2023}+1}{2021^{2022}+1}\)
so sánh
\(\dfrac{10^{2023}-3}{10^{2024}-3}\)
và
\(\dfrac{10^{2022}+1}{10^{2023}+1}\)
Ta có :
\(\dfrac{10^{2023}}{10^{2024}}=\dfrac{10^{2022}}{10^{2023}}\)
mà \(\dfrac{10^{2023}}{10^{2024}}>\dfrac{10^{2023}-3}{10^{2024}-3}\)
\(\dfrac{10^{2022}}{10^{2023}}< \dfrac{10^{2022}+1}{10^{2023}+1}\)
\(\Rightarrow\dfrac{10^{2023}-3}{10^{2024}-3}< \dfrac{10^{2022}+1}{10^{2023}+1}\)
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so sánh a, A=154/155+155/156 và B=154+155/155+156 b,C=2021+2022+2023/2022+2023+2024 và D =2021/2022+2022/2023=2023/2024
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so sánh a, A=154/155+155/156 và B=154+155/155+156 b,C=2021+2022+2023/2022+2023+2024 và D =2021/2022+2022/2023=2023/2024
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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
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bài 7 so sánh A và B
A=2022/2023 + 2023/2024 B=2022+2023/2023+2024
So sánh
a)17/20 và 18/19 b)19/18 và 2023/2022
c)13/17 và 135/175 d)53/63 và 535/636
e)13/15 và 22/25 \(\dfrac{2023}{2023^2+1}và\dfrac{2022}{2022^2+1}\)
a) \(\dfrac{17}{20}< \dfrac{18}{20}< \dfrac{18}{19}\Rightarrow\dfrac{17}{20}< \dfrac{18}{19}\)
b) \(\dfrac{19}{18}>\dfrac{19+2024}{18+2024}=\dfrac{2023}{2022}\Rightarrow\dfrac{19}{18}>\dfrac{2023}{2022}\)
c) \(\dfrac{135}{175}=\dfrac{27}{35}\)
\(\dfrac{13}{17}=\dfrac{26}{34}< \dfrac{26+1}{34+1}=\dfrac{27}{35}\)
\(\Rightarrow\dfrac{13}{17}< \dfrac{135}{175}\)
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so sánh c và d : C= \(\dfrac{2^{2024}-3}{2^{2023}-1}\) và D =\(\dfrac{2^{2023}-3}{2^{2022}-1}\)
\(C=\dfrac{2^{2024}-3}{2^{2023}-1}=\dfrac{2.2^{2023}-2-1}{2^{2023}-1}=\dfrac{2\left(2^{2023}-1\right)-1}{2^{2023}-1}=2-\dfrac{1}{2^{2023}-1}\)
\(D=\dfrac{2^{2023}-3}{2^{2022}-1}=\dfrac{2.2^{2022}-2-1}{2^{2022}-1}=\dfrac{2\left(2^{2022}-1\right)-1}{2^{2022}-1}=2-\dfrac{1}{2^{2022}-1}\)
Ta có
\(2^{2023}>2^{2022}\Rightarrow2^{2023}-1>2^{2022}-1\)
\(\Rightarrow\dfrac{1}{2^{2023}-1}< \dfrac{1}{2^{2022}-1}\Rightarrow2-\dfrac{1}{2^{2023}-1}>2-\dfrac{1}{2^{2022}-1}\)
\(\Rightarrow C>D\)
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