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\(A=\frac{2005}{2006}+\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2005}=1-\frac{1}{2006}+1-\frac{1}{2007}+1-\frac{1}{2008}+1+\frac{1}{2005}\)
\(=\left(1+1+1+1\right)+\left(\frac{1}{2005}-\frac{1}{2006}-\frac{1}{2007}-\frac{1}{2008}\right)
![](https://rs.olm.vn/images/avt/0.png?1311)
2005/2006 +2006/2007+2007/2008+2008/2005
ta thấy 2006 giống 2006,2007 giống 2007, 2008 giống 2008 nên ta gạch các số 2006 với 2006,2007 với 2007,2008 với 2008
còn phân số 2005/2005
phân số 2005/2005 = 1
nên kết quả là 1
k mk nha
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta thấy:
2005/2006 = 1 - 1/2006
2006/2007 = 1 - 1/2007
2007/2008 = 1 - 1/2008
2008/2005 = 1 + 3/2005
Mà: 1/2005 > 1/2006 > 1/2007 > 1/2008
=> 3/2005 - 1/2006 - 1/2007 - 1/2008 > 0
=> 2005/2006 + 2006/2007 + 2007/2008 + 2008/2005 > 4
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\(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\)
\(=1-\frac{1}{9}=\frac{8}{9}\)
\(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\)
\(=1+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+\left(\frac{1}{7}-\frac{1}{7}\right)-\frac{1}{9}\)
\(=1-\frac{1}{9}=\frac{8}{9}\)
~ Hok tốt ~
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{2002}{2001}+\frac{2003}{2002}+\frac{2004}{2003}+\frac{2005}{2004}+\frac{2006}{2005}+\frac{2007}{2006}+\frac{2008}{2007}+\frac{2009}{2008}>\frac{2001}{2001}+\frac{2002}{2002}+\frac{2003}{2003}+\frac{2004}{2004}+\frac{2005}{2005}+\frac{2006}{2006}+\frac{2007}{2007}+\frac{2008}{2008}\)
\(A=\frac{2002}{2001}+\frac{2003}{2002}+\frac{2004}{2003}+\frac{2005}{2004}+\frac{2006}{2005}+\frac{2007}{2006}+\frac{2008}{2007}+\frac{2009}{2008}>1+1+1+1+1+1+1+1\)\(A=\frac{2002}{2001}+\frac{2003}{2002}+\frac{2004}{2003}+\frac{2005}{2004}+\frac{2006}{2005}+\frac{2007}{2006}+\frac{2008}{2007}+\frac{2009}{2008}>8\)
\(A>8\)
A= 2006*2010-2005 / 2007*2009-2008
A=4032060-2005 / 4032063-2008
A=4030055/4030055
A=1
2006* 2010-2005/{2006+1}*2009-2008