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2003/2004 + 2004/2005 + 2005/2003
= 1 - 1/2004 + 1 - 1/2005 + 1 + 1/2003 + 1/2003
=(1+1+1)-(1/2004 - 1/2003 + 1/2005 - 1/2003)
= 3 - (1/2004 - 1/2003 + 1/2005 - 1/2003)
Vì 1/2004 < 1/2003 ; 1/2005 < 1/2003
=>1/2004 - 1/2003 + 1/2005 - 1/2003 < 0
=> 3 - (...) > 3
Vậy. ...
K mình nha
\(\frac{2003}{2004}+\frac{2004}{2005}+\frac{2005}{2003}=1-\frac{1}{2004}+1-\frac{1}{2005}+1+\frac{2}{2003}\)
\(=3+\left(\frac{1}{2003}-\frac{1}{2004}\right)+\left(\frac{1}{2003}-\frac{1}{2005}\right)\)
Do \(\frac{1}{2003}>\frac{1}{2004}>\frac{1}{2005}.\) nên \(\left(\frac{1}{2003}-\frac{1}{2004}\right)+\left(\frac{1}{2003}-\frac{1}{2005}\right)>0\)
Vì vậy \(3+\left(\frac{1}{2003}-\frac{1}{2004}\right)+\left(\frac{1}{2003}-\frac{1}{2005}\right)>3\) (đpcm)
\(A=\frac{2003}{2004}+\frac{2004}{2005}+\frac{2005}{2003}\)
\(=(1-\frac{1}{2004})+(1-\frac{1}{2005})+(1+\frac{2}{2003})\)
\(=3+(\frac{1}{2003}+\frac{1}{2003}-\frac{1}{2004}-\frac{1}{2005})\)
Do\(\frac{1}{2003}\)>\(\frac{1}{2004}\)>\(\frac{1}{2005}\)
\(\Rightarrow\frac{1}{2003}+\frac{1}{2003}+\frac{1}{2004}+\frac{1}{2005}\)>\(0\)
\(\Rightarrow3+(\frac{1}{2003}-\frac{1}{2004}+\frac{1}{2003}-\frac{1}{2005})\)>\(3\)
\(\Rightarrow A\)>\(3\)
a) \(\frac{2005.2007-1}{2004+2005.2006}=\frac{\left(2014+1\right).2007-1}{2004+2005.2006}=\frac{2004+2005.2007-1}{2004+2005-2006}=\frac{2004+2005.2006}{2004+2005.2006}=1\)
Ta có:\(A=2004\times15+2004\times6-2004\)
\(=2004\times\left(15+6-1\right)\)
\(=2004\times\left(21-1\right)=2004\times20\)
\(< 20\times2005=B\)
Nên \(A< B\)
2006/2007 lớn hơn 2005/2006
(bàn phím vừa bị đơ dấu lớn, thông cảm)
chọn mìn nha