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Ta có :
\(A=\dfrac{2019\times2020}{2019\times2020+1}=\dfrac{2019\times2020+1-1}{2019\times2020+1}=1-\dfrac{1}{2019\times2020+1}\)
Suy ra A < 1 (1)
Lại có \(B=\dfrac{2020}{2019}=\dfrac{2019+1}{2019}=\dfrac{2019}{2019}+\dfrac{1}{2019}=1+\dfrac{1}{2019}\)
Suy ra B > 1 (2)
Từ (1) và (2) ta có : A < 1 < B
=> A < B
Vậy A < B
\(\left(2020\frac{2018}{2021}-2019\frac{20182018}{20212021}\right):\frac{2018}{2021}\)
\(=\left(2020\frac{2018}{2021}-2019\frac{2018}{2021}\right):\frac{2018}{2021}\)
\(=1:\frac{2018}{2021}=\frac{2021}{2018}\)
ko ghi lại đề
ta thấy : 2019 - 1 = 2018
2020 - 2 = 2018
2021 - 3 = 2018
2022 - 4 = 2018
=> x = 2018
thử lại :
2018+1/2019 + 2018+2/2020 = 2018+3/2021 + 2018+4/2022
= 1 + 1 = 1 + 1
2 = 2
vi 2018/2019<1
2019/2020<1
2020/2021<1
nen 2018/2019 + 2019/2020 + 2020/2021<1+1+1=3
Ta có:
\(A=\frac{2021^{2021}+1}{2021^{2022}+1}\Leftrightarrow10A=\frac{2021^{2022}+10}{2021^{2022}+1}=1+\frac{9}{2021^{2022}+1}\)
\(B=\frac{2021^{2022}-1}{2021^{2023}-1}\Leftrightarrow10B=\frac{2021^{2023}-10}{2021^{2023}-1}=1-\frac{9}{2021^{2023}-1}\)
Hay ta đang so sánh: \(\frac{9}{2021^{2022}};\frac{9}{2021^{2023}}\)
Mà \(\frac{9}{2021^{2022}}>\frac{9}{2021^{2023}}\)nên \(\frac{2021^{2021}+1}{2021^{2022}+1}>\frac{2021^{2022}-1}{2021^{2023}-1}\)hay\(A>B\)
Vậy \(A>B\)
Dấu ''\(x\)'' là dấu nhân chăng ?
\(A=\frac{2019x2020}{2019x2020+1}\)và \(B=\frac{2020}{2021}\)
Bài ra ta có :
Xét \(A=\frac{2019x2020}{2019x\left(2020+1\right)}=\frac{2020}{2020+1}=\frac{2020}{2021}\)
Vì \(\frac{2020}{2021}=\frac{2020}{2021}\)
Suy ra A = B theo (ĐPCM)