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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 ~
\(\frac{2010}{2011}\)> \(\frac{2010}{2011+2012+2013}\)
\(\frac{2011}{2012}\)> \(\frac{2011}{2011+2012+2013}\)
\(\frac{2012}{2013}\)> \(\frac{2012}{2011+2012+2013}\)
=> \(\frac{2010}{2011}\)+ \(\frac{2011}{2012}\)+ \(\frac{2012}{2013}\)> \(\frac{2010+2011+2012}{2011+2012+2013}\)
=> P > Q
AM-GM:\(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}+\frac{2013}{2010}\ge4\sqrt[4]{\frac{2010.2011.2012.2013}{2011.2012.2013.2010}}=4\sqrt[4]{1}=4\)
\(\Rightarrow S\ge4\)
^^
Ta có : Q=2010/2011+2012+2013 + 2011/2011+2012+2013 +2012/2011+2012+2013
Đó là bước đầu còn phần sau bạn tự so sánh từng phân số của P và Q nhé, k cho mik!
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)
\(\Rightarrow B>A\)
P = \(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\)
Q = \(\frac{2010+2011+2012}{2011+2012+2013}\) = \(\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
Vì: \(\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\)
\(\frac{2011}{2012}>\frac{2011}{2011+2012+2013}\)
\(\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\)
=> \(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}>\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
P > Q
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??????????
P=\(\frac{2012-1}{2012}+\frac{2013-1}{2013}+\frac{2014-1}{2014}+\frac{2015-1}{2015}\)
=\(1-\frac{1}{2012}+1-\frac{1}{2013}+1-\frac{1}{2014}+1-\frac{1}{2015}\)
=\(4-\left(\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}+\frac{1}{2015}\right)\)
VẬY P<4
\(\orbr{\begin{cases}\orbr{\begin{cases}\frac{2011}{2012}< 1\\\frac{2012}{2013}< 1\end{cases}}\\\orbr{\begin{cases}\frac{2013}{2014}< 1\\\frac{2014}{2015}< 1\end{cases}}\end{cases}\Rightarrow P< 1+1+1+1=4}\)
=1-1/2012+1-1/2013+1+2/2011
=(1+1+1)-1/2012-1/2013+2/2011
=3-1/2012-1/2013+2/2011
ta co: 1/2011>1/2012>1/2013
vay 2011/2012+2012/2013+2013/2011>3