Ta có : \(\frac{2011}{2012}=1-\frac{1}{2012}\)

           \(\frac{2012}{2013}=1-\frac{1}{2013}\)

            \(\frac{2013}{2011}=1+\frac{2}{2011}\)

Ta có : \(\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2011}=\left(1-\frac{1}{2012}\right)+\left(1-\frac{1}{2013}\right)+\left(1+\frac{2}{2011}\right)\)

       =   \(\left(1+1+1\right)+\left(\frac{2}{2011}-\frac{1}{2012}-\frac{1}{2013}\right)\)

       =  \(3+\frac{2}{2011}-\left(\frac{1}{2012}+\frac{1}{2013}\right)\)

Ta có :  

\(\frac{1}{2012}+\frac{1}{2013}< \frac{1}{2012}+\frac{1}{2012}=\frac{2}{2012}\)

mà : \(\frac{2}{2012}< \frac{2}{2011}=>\frac{1}{2012}+\frac{1}{2013}< \frac{2}{2011}\)

=> \(\frac{2}{2011}-\left(\frac{1}{2012}+\frac{1}{2013}\right)>0\)

Vậy : \(3+\frac{2}{2011}-\left(\frac{1}{2012}+\frac{1}{2013}\right)>3\)

Vậy : \(\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2011}>3\)

ủng hộ mik nhá các bạn ơiii ^_^"

Có : \(\frac{2011}{2012}=\frac{2012-1}{2012}=1-\frac{1}{2012}\)

Có : \(\frac{2012}{2013}=\frac{2013-1}{2013}=1-\frac{1}{2013}\)

Có : \(\frac{2013}{2011}=\frac{2011+2}{2011}=1+\frac{2}{2011}\)

Cộng vế với vế ta có : \(\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2011}=1-\frac{1}{2012}+1-\frac{1}{2013}+1+\frac{2}{2011}=1+1+1-\left(\frac{1}{2012}+\frac{1}{2013}-\frac{2}{2011}\right)=3-\left(\frac{1}{2012}+\frac{1}{2013}-\frac{2}{2011}\right)\)

Vì \(\frac{1}{2012}+\frac{1}{2013}-\frac{2}{2011}>0\) nên \(3-\left(\frac{1}{2012}+\frac{1}{2013}-\frac{2}{2011}\right)<3\)

Vậy \(\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2011}<3\)

Bài nãy sai rồi, cho mình làm lại nha:

\(\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2011}=\frac{2012-1}{2012}+\frac{2013-1}{2013}+\frac{2011+1+1}{2011}\)

\(=1-\frac{1}{2012}+1-\frac{1}{2013}+1+\frac{1}{2011}\)

Vì: \(\frac{1}{2011}>\frac{1}{2012}>\frac{1}{2013}\Rightarrow\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2012}+\frac{1}{2012}>0\)

\(\Rightarrow\frac{2012-1}{2012}+\frac{2013-1}{2013}+\frac{2011+1+1}{2011}>3\)

Nên \(\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2011}>3\)

chịu........

Áp dụng tỉ dãy số bằng nhau, ta có:

\(\frac{2011+2012-2013}{2012+2013-2011}=\frac{2011-2012+2013}{2012+2013-2011}=\frac{2011-2012+2013}{-2011-2012+2013}=\left(-1\right)\)

2011/2012+2012/2013+2013/2011

=2011/2012+2012/2013+1+2/2011

(1/2011+2011/2012)+(2012/2013+1/2012)+1

Vì 1/2011<1/2012 nên 1/2011+2011/2012<1

Vì 1/2011<1/2013 nên 1/2011+2012/2013<1

Suy ra C>1+1+1=3

Vậy C>3

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 .

Ta có :

B = 2012201320122013 .

       20112012+201320112012+2013 .

        20122012+201320122012+2013 .

 A < B .

Giải:

Ta có:

\(A=\dfrac{2011+2012}{2012+2013}\) 

\(A=\dfrac{2011}{2012+2013}+\dfrac{2012}{2012+2013}\) 

Vì \(\dfrac{2011}{2012}>\dfrac{2011}{2012+2013}\)  

\(\dfrac{2012}{2013}>\dfrac{2012}{2012+2013}\)

\(\Rightarrow A< B\)

Câu trả lời:A<B

\(\frac{2010+2011+2012}{2011+2012+2013}=\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)

Vì \(\frac{2010}{2011+2012+2013}<\frac{2010}{2011};\frac{2011}{2011+2012+2013}<\frac{2011}{2012};\frac{2012}{2011+2012+2013}<\frac{2012}{2013}\)

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