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`a,`
`5/6=1-1/6`
`7/8=1-1/8`
Mà `1/6>1/8 -> 5/6<7/8`
`b,`
`9/5=(9 \times 2)/(5 \times 2)=18/10`
`3/2=(3 \times 5)/(2 \times 5)=15/10`
`18/10 > 15/10 -> 9/5 > 3/2`
`c,`
`2017/2018 = 1-1/2018`
`2019/2020=1-1/2020`
`1/2018 > 1/2020 -> 2017/2018 < 2019/2020`
`d,`
`2018/2017 = 1+1/2017`
`2020/2019 = 1+1/2019`
`1/2017 > 1/2019 -> 2018/2017>2020/2019`
![](https://rs.olm.vn/images/avt/0.png?1311)
tớ nghĩ là các phân số trên đều là những ps nhỏ hơn 1 lên A<3
mình chỉ nghĩ thôi. K biết đúng hay sai đâu. đúng thì tích còn sai thì bỏ qua cho
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M = 1/3.5 + 1/5.7 + 1/7.9 + ... + 1/2017.2019
M = 1/2.(1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ... + 1/2017 - 1/2019)
M = 1/2.(1/3 - 1/2019)
M = 1/2.224/673
M = 112/673
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(1-\frac{2017}{2018}=\frac{1}{2018};1-\frac{2018}{2019}=\frac{1}{2019};1-\frac{2019}{2020}=\frac{1}{2020}\)
Vì \(\frac{1}{2018}>\frac{1}{2019}>\frac{1}{2020}\)nên \(\frac{2017}{2018}< \frac{2018}{2019}< \frac{2019}{2020}\)
2017/2018 = (2018-1)/2018 = 1-1/2018
2018/2019 = (2019-1)/2019 = 1 - 1/2019
2019/2020 = (2020-1)/2020 = 1 - 1/2020
Có 1/2018 > 1/2019 > 1/2020 => 2017/2018 < 2018/2019 < 2019/2020
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\dfrac{2020}{2019}-\dfrac{2019}{2018}+\dfrac{1}{2018\times2019}\)
\(A=\dfrac{2020}{2019}-\dfrac{2019}{2018}+\dfrac{1}{2018}-\dfrac{1}{2019}\)
\(A=\left(\dfrac{2020}{2019}-\dfrac{1}{2019}\right)-\left(\dfrac{2019}{2018}-\dfrac{1}{2018}\right)\)
\(A=\left(\dfrac{2020-1}{2019}\right)-\left(\dfrac{2019-1}{2018}\right)\)
\(A=1-1\)
\(A=0.\)
\(A=\dfrac{2020}{2019}-\dfrac{2019}{2018}+\dfrac{1}{2018\times2019}\)
\(A=\dfrac{2020}{2019}-\dfrac{2019}{2018}+\dfrac{1}{2018}-\dfrac{1}{2019}\)
\(A=\left(\dfrac{2020}{2019}-\dfrac{1}{2019}\right)-\left(\dfrac{2019}{2018}-\dfrac{1}{2018}\right)\)
\(A=\dfrac{2019}{2019}-\dfrac{2018}{2018}\)
\(A=1-1\)
\(A=0\)
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Ta có: \(\frac{2018}{2019}\)+ \(\frac{2019}{2020}\)+\(\frac{2020}{2018}\)= (1-\(\frac{1}{2019}\)) + ( 1 -\(\frac{1}{2020}\)) + ( 1 - \(\frac{1}{2018}\)) = ( 1+1+1) - (\(\frac{1}{2019}+\frac{1}{2020}+\frac{1}{2018}\)) = 3 - (\(\frac{1}{2019}+\frac{1}{2020}+\frac{1}{2018}\)) \(\Leftrightarrow\)3 - (\(\frac{1}{2019}+\frac{1}{2020}+\frac{1}{2018}\)) <3 Vậy \(\frac{2018}{2019}+\frac{2019}{2020}+\frac{2020}{2018}\)< 3
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=2018\times2020+2021\) và \(B=2019\times2019+2021\)
\(A=2018\times2019+2018+2021\)
\(B=2018\times2019+2019+2021\)
Vì \(2019>2018\Rightarrow A< B\)
Trả lời
Chắc chắn A > B rồi !
HIHI hok tốt !
Ta có:
\(A=\frac{2018+2019}{2019+2020}=\frac{2018}{2019+2020}+\frac{2019}{2019+2020}\)
mà 2019+2020 >2019>2020 \(\Rightarrow\frac{2018}{2019+2020}< \frac{2018}{2019};\frac{2019}{2019+2020}< \frac{2019}{2020}\)
\(\Rightarrow\frac{2018}{2019+2020}+\frac{2019}{2019+2020}< \frac{2018}{2019}+\frac{2019}{2020}\)hay \(A< B\)