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\(A=\frac{2010}{2009}+\frac{2011}{2010}+\frac{2012}{2011}+\frac{2009}{2012}=\left(1+\frac{1}{2009}\right)+\left(1+\frac{1}{2010}\right)+\left(1+\frac{1}{2011}\right)+\frac{2009}{2012}>\left(1+\frac{1}{2012}\right)+\left(1+\frac{1}{2012}\right)+\left(1+\frac{1}{2012}\right)+\frac{2009}{2012}=\left(1+1+1\right)+\left(\frac{1}{2012}+\frac{1}{2012}+\frac{1}{2012}+\frac{2009}{2012}\right)=3+1=4\)Vì 1/2009,1/2010,1/2011>1/2012
Vậy A>4
A=(1+1/2009)+(1+1/2010)+(1+1/2011)+(1-3/2012)
A=(1+1+1+1)+(1/2009+1/2010+1/2011-3/2012)
A=4+(1/2009+1/2010+1/2011-3x1/2012)
vì 1/2009>1/2010>1/2011>1/2012
nên 3x1/2012>(1/2009+1/2010+1/2011)
hay 3x1/2012-(1/2009+1/2010+1/2011)>0