\(\dfrac{2011}{2010}< \dfrac{2011+1}{2010+1}=\dfrac{2012}{2011}\)
\(\Rightarrow\dfrac{2011}{2010}< \dfrac{2012}{2011}\)
\(\dfrac{2012}{2011}và\dfrac{2011}{2010}\\ \dfrac{2012}{2011}-1=\dfrac{1}{2011}\\ \dfrac{2011}{2010}-1=\dfrac{1}{2010}\\ \)
Vì \(\dfrac{1}{2011}< \dfrac{1}{2010}\\ \Rightarrow\dfrac{2012}{2011}< \dfrac{2011}{2010}\)
\(\dfrac{2012}{2011}\) = 1 + \(\dfrac{1}{2011}\); \(\dfrac{2011}{2010}\) = 1 + \(\dfrac{1}{2010}\)
Vì \(\dfrac{1}{2011}\) < \(\dfrac{1}{2010}\)
Nên \(\dfrac{2012}{2011}\) < \(\dfrac{2011}{2010}\)
2012/2011 = 1 + 1/2011
2011/2010 = 1 + 1/2010
Do 2011 > 2010
⇒ 1/2011 < 1/2010
⇒ 1 + 1/2011 < 1 + 1/2010
Vậy 2012/2011 < 2011/2010
