Question

So sánh P và Q biết:

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

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

Answer 1

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 ~ 

Answer 2

Trl :

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Học tốt nhé bạn @