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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)
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\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2019.2020}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{2019}-\frac{1}{2020}\)
\(=1-\frac{1}{2020}>1\)
\(\frac{2019}{2020}+\frac{2020}{2019}=1-\frac{1}{2020}+1+\frac{1}{2019}\)
\(=2+\frac{1}{2019}-\frac{1}{2020}\)
Vì \(\frac{1}{2019}>\frac{1}{2020}\Rightarrow\frac{1}{2019}-\frac{1}{2020}>0\)
\(\Rightarrow2+\frac{1}{2019}-\frac{1}{2020}>2\)
\(\frac{444443}{222222}=\frac{444444}{222222}-\frac{1}{222222}=2-\frac{1}{222222}< 2\)
\(\Rightarrow\frac{2019}{2020}+\frac{2020}{2019}>\frac{444443}{222222}\)
\(C=\dfrac{2}{1\times2}+\dfrac{2}{2\times3}+...+\dfrac{2}{2019\times2020}\)
\(=2\left(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+...+\dfrac{1}{2019\times2020}\right)\)
\(=2\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2019}-\dfrac{1}{2020}\right)\)
\(=2\left(1-\dfrac{1}{2020}\right)=2.\dfrac{2019}{2020}=\dfrac{2019}{1010}\)
A=1-1/2019+1-1/2020+1+2/2018
=>A=(1+1+1)+(1/2018-1/2009)+(1/2018-1/2020)
Vì 1/2018>1/2019 và 1/2028>1/2020
=>A>3
Vậy a >A
study well
k nha ủng hộ mk nhé
Mình cũng làm giống thế . nhưng con bạn mình làm a < 3 nên mình không chắc chắn
\(Ta\)có :\(a\)=\(\frac{2017\cdot2018-1}{2017.2018}\)=\(\frac{2017.2018}{2017.2018}\)-\(\frac{1}{2017.2018}\)=1-\(\frac{1}{2017.2018}\)
\(b\)=\(\frac{2019.2020-1}{2019.2020}\)=\(\frac{2019.2020}{2019.2020}\)-\(\frac{1}{2019.2020}\)=1-\(\frac{1}{2019.2020}\)
Vì \(\frac{1}{2018.2019}\)> \(\frac{1}{2019.2020}\)nên \(a\)< \(b\)(sử dụng phần bù)
so sánh a và b biết a=2017×2018−12017×20182017×20182017×2018−1và b =2019×2020−12019×20202019×20202019×2020−1
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