Lời giải:
Câu 1.
$P=\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}$,ta có:
$\frac{2010}{2011}<\frac{2011}{2011}$
$\frac{2011}{2012}<\frac{2012}{2012}$<=>$\frac{2011}{2012}<\frac{2011}{2011}$(Vì $\frac{2012}{2012}=\frac{2011}{2011}$)
$\frac{2012}{2013}<\frac{2013}{2013}$<=>$\frac{2012}{2013}<\frac{2011}{2011}$(Vì $\frac{2013}{2013}=\frac{2011}{2011}$)
$=>P<3.\frac{2011}{2011}$
$Q=\frac{2010+2011+2012}{2011+2012+2013}<\frac{2011+2012+2013}{2011+2012+2013}$<=>$\frac{2010+2011+2012}{2011+2012+2013}<\frac{2011}{2011}$(Vì $\frac{2011+2012+2013}{2011+2012+2013}=\frac{2011}{2011}$)
Mà: $3.\frac{2011}{2011}>\frac{2011}{2011}$=>$P>Q$
(Lưu ý:Mẫu lớn hơn tử $<1$ và ngược lại $>1$)