so sánh các phân số:
1.2011/2012 và 2012/2011
2.2000/2013 và 2011/2012
K
Khách
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Những câu hỏi liên quan
BV
3
7 tháng 6 2021
Ta có :
B = \(\dfrac{2011}{2012}\) + \(\dfrac{2012}{2013}\) .
\(\dfrac{2011}{2012}\) > \(\dfrac{2011}{2012+2013}\) .
\(\dfrac{2012}{2013}\) > \(\dfrac{2012}{2012+2013}\) .
\(\Rightarrow\) A < B .
ND
1
H
21
14 tháng 6 2015
bạn tham khảo:
2010/2011+2012+2013 > 2010+2011+2012/2011+2012+2013
2011/2011+2012+2013 > 2010+2011+2012/2011+2012+2013
2012/2011+2012+2013 > 2010+2011+2012/2011+2012+2013
=> 2010/2011+2011/2012+2012/2013 > 2010+2011+2012/2011+2012+2013
14 tháng 6 2015
2010/2011+2012+2013 > 2010+2011+2012/2011+2012+2013
2011/2011+2012+2013 > 2010+2011+2012/2011+2012+2013
2012/2011+2012+2013 > 2010+2011+2012/2011+2012+2013
=> 2010/2011+2011/2012+2012/2013 > 2010+2011+2012/2011+2012+2013
BT
0
ES
2
3 tháng 9 2016
\(P=\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\)
\(P>\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
\(P>\frac{2010+2011+2012}{2011+2012+2013}\)
\(P>Q\)
17 tháng 5 2022
\(Q=\dfrac{2010+2011+2012}{2011+2012+2013}=\dfrac{2010}{2011+2012+2013}+\dfrac{2011}{2011+2012+2013}+\dfrac{2012}{2011+2012+2013}\)
Ta có: \(\dfrac{2010}{2011+2012+2013}< \dfrac{2010}{2011}\)
\(\dfrac{2011}{2011+2012+2013}< \dfrac{2011}{2012}\)
\(\dfrac{2012}{2011< 2012< 2013}< \dfrac{2012}{2013}\)
\(\Rightarrow\dfrac{2010}{2011+2012+2013}+\dfrac{2011}{2011+2012+2013}+\dfrac{2012}{2011+2012+2013}\)
\(\dfrac{2010}{2011}+\dfrac{2011}{2012}+\dfrac{2012}{2013}\)
\(P>Q\)
A
16 tháng 6 2018
Ta có \(\frac{2012.2013}{2012.2013+1}\)và \(\frac{2013}{2012}\)
Vì \(\frac{2012.2013}{2012.2013+1}< 1< \frac{2013}{2012}\)
nên \(\frac{2012.2013}{2012.2013+1}< \frac{2013}{2012}\)
\(\frac{2012}{2013}\)và \(\frac{2011}{2012}\)
phàn bù của \(\frac{2012}{2013}\)là \(\frac{1}{2013}\)
phàn bù của \(\frac{2011}{2012}\)là \(\frac{1}{2012}\)
Vì \(\frac{1}{2012}>\frac{1}{2013}\Rightarrow\frac{2012}{2013}>\frac{2011}{2012}\)
16 tháng 6 2018
Ta có : \(\frac{2012\cdot2013}{2012\cdot2013+1}< 1\)
\(\frac{2013}{2012}>1\)
\(\Rightarrow\frac{2012\cdot2013}{2012\cdot2013+1}< \frac{2013}{2012}\)
Có : \(\frac{2012}{2013}=1-\frac{2012}{2013}=\frac{2013}{2013}-\frac{2012}{2013}=\frac{1}{2013}\)
\(\frac{2011}{2012}=1-\frac{2011}{2012}=\frac{2012}{2012}-\frac{2011}{2012}=\frac{1}{2012}\)
Vì \(2013< 2012\)nên \(\frac{1}{2013}< \frac{1}{2012}\)hay \(\frac{2012}{2013}< \frac{2011}{2012}\)
TP
4
1, Ta thấy \(\frac{2011}{2012}< \frac{2012}{2012}=1\)(1)
Ta có :\(\frac{2012}{2011}>\frac{2011}{2011}=1\) (2 )
Từ (1) và (2) suy ra \(\frac{2011}{2012}< 1< \frac{2012}{2011}\)hay \(\frac{2011}{2012}< \frac{2012}{2011}\)
Vậy \(\frac{2011}{2012}< \frac{2012}{2011}\)
2, Ta thấy \(\frac{2000}{2013}=\frac{2013-3}{2013}=\frac{2013}{2013}-\frac{3}{2013}=1-\frac{3}{2013}\)
\(\frac{2011}{2012}=\frac{2012-1}{2012}=\frac{2012}{2012}-\frac{1}{2012}=1-\frac{1}{2012}\)
Ta có \(\frac{1}{2012}=\frac{3}{6036}< \frac{3}{2013}\)nên \(\frac{1}{2012}< \frac{3}{2013}\)suy ra \(1-\frac{3}{2013}< 1-\frac{1}{2012}\)
Hay \(\frac{2000}{2013}< \frac{2011}{2012}\)
Vậy \(\frac{2000}{2013}< \frac{2011}{2012}\)