A = \(\frac{2011+2012}{2012+2013}=\frac{2011+2012}{4025}\)

Ta có:

\(\frac{2011}{2012}>\frac{2011}{4025}\)

\(\frac{2012}{2013}>\frac{2012}{4025}\)

=> \(\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{4025}+\frac{2012}{4025}\)

=> \(B>\frac{2011+2012}{4025}\)

=>\(B>A\)

bạn xem ở đây nhé

Đây

A = B

mình giỏi lắm

IQ vô cực

Ta có : \(Q=\frac{2010+2011+2012}{2011+2012+2013}\)

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

Mà \(\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\)

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

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

Cộng vế theo vế, ta có : \(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}>\frac{2010+2011+2012}{2011+2012+2013}\)

\(\Rightarrow P>Q\)

Ta có:

2010/2011 >2010/2011+2012+2013. ;2011/2012 >2011/2011+2012+2013 .;2012/2013 >2012/2011+2012+2013 ->2010/2011+2011/2012+2012/2013 >2010+2011+2012/2011+2012+2013. Vậy P > Q

thanks các bạn nhìu nha

TA CÓ :

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

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

VÌ : \(\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\)

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

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

=> A > B 

VẬY , A > B

Mình tự hỏi. sao banh biết rồi còn đăng lên làm gì??????????

CÁCH CỦA MÌNH LÀ HOÀN TOÀN ĐÚNG NHA !

Ta có \(B=\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2013}+\frac{2012}{2013}=\frac{2011+2012}{2013}\)

    Lại có: \(\frac{2011+2012}{2013}>\frac{2011+2012}{2012+2013}\)                        ( ngoặc 2 dòng này lại nhé dòng này và dòng trên)

 \(\Rightarrow B>A\)

nhầm là A > B

Gọi 2011 là a

2012 là b;2013 là c

=>\(A=\frac{2011}{2012}+\frac{2012}{2013}=\frac{a}{b}+\frac{b}{c}\);\(B=\frac{2011+2013}{2012+2013}=\frac{a+c}{b+c}\)

=>\(A=\frac{a}{b}+\frac{b}{c}=\frac{ac+b^2}{bc}\)\(=\frac{\left(ac+b^2\right).\left(b+c\right)}{bc.\left(b+c\right)}\);\(B=\frac{a+c}{b+c}=\frac{\left(a+c\right).bc}{bc.\left(b+c\right)}\)

b+c>a+c;b²+ac>bc

Vậy A>B

ta có: \(\frac{2011}{2012}>\frac{2011}{2012+2013};\frac{2012}{2013}>\frac{2012}{2013+2012}.\)

\(\Rightarrow A>\frac{2011}{2012+2013}+\frac{2012}{2013+2012}=\frac{2011+2012}{2012+2013}=B\)

....

Ta có \(\frac{2011}{2012}>\frac{2011}{2012+2013}\)

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

CỘNG VẾ THEO VẾ,TA CÓ:

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

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

\(\Rightarrow A>B\)

Vậy A>B

Ta có: \(A>1\)

         \(B<1\)

=> \(A>B\)

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

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

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

nên A <B

Ta có

\(\frac{A^{2011}}{A^{2012}}=\frac{A^{2012}}{A^{2103}}=\frac{A}{A^2}\)

=> \(\frac{A^{2011}}{A^{2012}}+\frac{A^{2012}}{A^{2013}}=\frac{2A}{A^2}\)

\(\frac{A^{2011+2012}}{A^{2012+2013}}=\frac{A^{4023}}{A^{4025}}=\frac{1}{A^2}\)

=> \(\frac{A^{2011+2012}}{A^{2012+2013}}< \frac{A^{2011}}{A^{2012}}+\frac{A^{2012}}{A^{2013}}\)

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

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

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

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

=> P > Q