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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)
\(\Rightarrow B>A\)
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??????????
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
\(\frac{A^{2011}}{A^{2012}}=\frac{A^{2012}}{A^{2103}}=\frac{A}{A^2}\)
=> \(\frac{A^{2011}}{A^{2012}}+\frac{A^{2012}}{A^{2013}}=\frac{2A}{A^2}\)
\(\frac{A^{2011+2012}}{A^{2012+2013}}=\frac{A^{4023}}{A^{4025}}=\frac{1}{A^2}\)
=> \(\frac{A^{2011+2012}}{A^{2012+2013}}< \frac{A^{2011}}{A^{2012}}+\frac{A^{2012}}{A^{2013}}\)
\(\frac{2010}{2011}\)> \(\frac{2010}{2011+2012+2013}\)
\(\frac{2011}{2012}\)> \(\frac{2011}{2011+2012+2013}\)
\(\frac{2012}{2013}\)> \(\frac{2012}{2011+2012+2013}\)
=> \(\frac{2010}{2011}\)+ \(\frac{2011}{2012}\)+ \(\frac{2012}{2013}\)> \(\frac{2010+2011+2012}{2011+2012+2013}\)
=> P > Q
Ta có :
\(Q=\frac{2010+2011+2012}{2011+2012+2013}=\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
Vì :
\(\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\)
\(\frac{2011}{2012}>\frac{2011}{2011+2012+2013}\)
\(\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\)
Nên \(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}>\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
\(\Rightarrow\)\(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}>\frac{2010+2011+2012}{2011+2012+2013}\)
\(\Rightarrow\)\(P>Q\)
Vậy \(P>Q\)
Chúc bạn học tốt ~
A= \(\frac{2011}{2013}\)
B=\(\frac{2011}{2013}\)
vì bạn có thấy cả mẫu và tử đều có 2012 nên bạn gạch nó đi cả A:B đều vạy
vậy A và B bằng nhau
ai đi qua đồng tình thì nhé
A=\(\frac{2011+2012}{2012+2013}=\frac{2011}{2012+2013}+\frac{2012}{2012+2013}\)
Vì \(\frac{2011}{2012+2013}<\frac{2011}{2012};\frac{2012}{2012+2013}<\frac{2012}{2013}\)
=>\(\frac{2011+2012}{2012+2013}<\frac{2011}{2012}+\frac{2012}{2013}\)
ta có:\(\frac{2011+2012}{2012+2013}=\frac{2011}{2012+2013}+\frac{2012}{2012+2013}\)
vì \(\frac{2011}{2012+2013}<\frac{2011}{2012};\frac{2012}{2012+2013}<\frac{2012}{2013}\)
=>A<B
A=2011/2012+2013+2012/2012+2013