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\(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2006}\)
\(A=1-\frac{1}{2007}+1-\frac{1}{2008}+1-\frac{2}{2006}\)
\(A=\left(1+1+1\right)+\left(\frac{1}{2006}-\frac{1}{2007}\right)+\left(\frac{1}{2006}-\frac{1}{2008}\right)\)
\(A=3+\left(\frac{1}{2006}-\frac{1}{2007}\right)+\left(\frac{1}{2006}-\frac{1}{2008}\right)\)
Ta thấy : \(\frac{1}{2006}-\frac{1}{2007}>0\); \(\frac{1}{2006}-\frac{1}{2008}>0\)\(\Rightarrow A>3\)
Ta có: 3 = 1 + 1 + 1
Ta có: 2006/2007 < 1 ; 2007/2008 < 1 ; 2008/2009 < 1
Nên 2006/2007 + 2007/2008+ 2008/2009 < (1+1+1=3)
Ta có: \(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2006}\)
\(A=1-\frac{1}{2007}+1-\frac{1}{2008}+1-\frac{2}{2006}\)
\(A=3+\frac{1}{2006}-\frac{1}{2007}+\frac{1}{2006}-\frac{1}{2008}>3\)
Vậy A > 3
\(\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2006}\)
\(\Rightarrow\frac{2008}{2006}>1\)
\(\frac{2006}{2007}< 1;\frac{2007}{2008}< 1\)
\(\Rightarrow\frac{2006}{2007}+\frac{2007}{2008}< 2\)
\(\Rightarrow\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2006}< 3\)
A =2006/2007+2007/2008+2008/2006
= \(\frac{2006}{2007}\)+ \(\frac{2007+1}{2008}\)+ \(\frac{2008}{2006+2}\)
= 1 - \(\frac{1}{2007}\)+ 1 - \(\frac{1}{2008}\)+ 1 + \(\frac{1}{2006}\)+ \(\frac{1}{2006}\)
= 3 + ( \(\frac{1}{2006}\)- \(\frac{1}{2007}\)) + ( \(\frac{1}{2006}\)- \(\frac{1}{2008}\))
vì \(\frac{1}{2006}\)> \(\frac{1}{2007}\), \(\frac{1}{2006}\)> \(\frac{1}{2008}\)nên A > 3