Ta có: \(\frac{2010}{2011}>\frac{2010}{2011+2012}\)

\(\frac{2011}{2012}>\frac{2011}{2011+2012}\)

Nên \(\frac{2010}{2011}+\frac{2011}{2012}>\frac{2010+2011}{2011+2012}\)\(\Rightarrow A>B\)

So sánh: \(\frac{2010}{2011}+\frac{2011}{2012}\) với \(\frac{2010+2011}{2011+2012}\)

Sao hông thêm 2 cái nữa cho tròn 440 luôn

ta có : 

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

ta có : \(\frac{2010}{2011}>\frac{2010}{2011+2012}\)

            \(\frac{2011}{2012}>\frac{2011}{2011+2012}\)

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

hay A>B

\(A=\left(1-\frac{1}{2011}\right)-\left(1-\frac{1}{2012}\right)+\left(1-\frac{1}{2013}\right)-\left(1-\frac{1}{2014}\right)\)

\(=1-\frac{1}{2011}-1+\frac{1}{2012}+1-\frac{1}{2013}-1+\frac{1}{2014}\)

\(=\left(1-1+1-1\right)-\left(\frac{1}{2011}+\frac{1}{2012}-\frac{1}{2013}+\frac{1}{2014}\right)\)

còn lại bó tay @@ 

\(A=\frac{2010}{2011}-\frac{2011}{2012}+\frac{2012}{2013}-\frac{2013}{2014}\)

và 

\(B=\frac{1}{2010.2011}-\frac{1}{2012.2013}\)

Q=2010+2011+2012/2011+2012+2013

Q=2010/2011+2012+2013 + 2011/2011+2012+2013 + 2012/2011+2012+2013

TA CÓl: 2010/2011>2010/2011+2012+2013

             2011/2012>2011/2011+2012+2013

             2012/2013>2012/2011+2012+2013 

=> P>Q 

Mình thấy bạn làm đúng đó

Ng. Cu ly giỏi ghê

Có : \(2009+2010>\dfrac{2009}{2010}\) ; \(2011+2012>\dfrac{2011}{2012}\)

\(\dfrac{2011}{2010}>1\) ; \(\dfrac{2010}{2011}< 1\) \(\Rightarrow\dfrac{2011}{2010}>\dfrac{2010}{2011}\)

Ta có : \(2009+2010+\dfrac{2011}{2010}+2011+2012>\dfrac{2009}{2010}+\dfrac{2010}{2011}+\dfrac{2011}{2012}\)

\(\Leftrightarrow B>A\)

Hay \(A< B\)

bn cầm máy tính mà bấm sau đó rồi so sánh kết quả, nha

Bạn ơi cho mình hỏi. Đây có phải bài trog toán tuổi thơ ko? 

A = 1-1/2011+1-1/2012 = 2-(1/2011+1/2012) > 1 ( vì 1/2011+1/2012 < 1 )

B = 4021/4023 = 1-2/4023 < 1

=> A > B

k mk nha