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\(\frac{2006}{2007}< \frac{2007}{2007}=1\)
\(\frac{2007}{2008}< \frac{2008}{2008}=1\)
\(\frac{2008}{2009}< \frac{2009}{2009}=1\)
\(\Rightarrow a=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}< 1+1+1=3\)
\(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2009}\)
\(A=\left(1-\frac{1}{2007}\right)+\left(1-\frac{1}{2008}\right)+\left(1-\frac{1}{2009}\right)\)
\(A=\left(1+1+1\right)-\left(\frac{1}{2007}+\frac{1}{2008}+\frac{1}{2009}\right)\)
\(A=3-\left(\frac{1}{2007}+\frac{1}{2008}+\frac{1}{2009}\right)< 3\)
\(A=\frac{2006+2007}{2006.2007}=\frac{2006}{2006.2007}+\frac{2007}{2006.2007}=\frac{1}{2007}+\frac{1}{2006}\)
\(B=\frac{2007+2008}{2007.2008}=\frac{2007}{2007.2008}+\frac{2008}{2007.2008}=\frac{1}{2008}+\frac{1}{2007}\)
Vì \(\frac{1}{2007}+\frac{1}{2006}>\frac{1}{2008}+\frac{1}{2007}\)
=> \(A>B\)
\(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2006}=1-\frac{1}{2007}+1-\frac{1}{2008}+1+\frac{2}{2006}\)
\(=3-\frac{1}{2007}-\frac{1}{2008}+\frac{2}{2006}=3+\left(\frac{1}{2006}-\frac{1}{2007}+\frac{1}{2006}-\frac{1}{2008}\right)\)
Vì \(\frac{1}{2006}>\frac{1}{2007};\frac{1}{2006}>\frac{1}{2008}\Rightarrow\frac{1}{2006}-\frac{1}{2007}>0;\frac{1}{2006}-\frac{1}{2008}>0\)
Do đó \(\frac{1}{2006}-\frac{1}{2007}+\frac{1}{2006}-\frac{1}{2008}>0\)
\(\Rightarrow3+\left(\frac{1}{2006}-\frac{1}{2007}+\frac{1}{2006}-\frac{1}{2008}\right)>3\)
Vậy \(A>3\)
\(A=\frac{2006}{2007}+\frac{2007}{2008}+\frac{2008}{2006}=1-\frac{1}{2007}+1-\frac{1}{2008}+1-\frac{2}{2006}=3+\left(\frac{1}{2006}-\frac{1}{2007}\right)+\left(\frac{1}{2006}-\frac{1}{2008}\right)\)\(>3+\left(\frac{1}{2007}-\frac{1}{2007}\right)+\left(\frac{1}{2008}-\frac{1}{2008}\right)=3=>A>3\)
Bài 1
=1093/2187
Bai 2
số nhỏ nhất trong các số trên là:2007/2008
Bai 3
Ta co :111111/151515=11/15 & 11032/15030=11/15
vì 11/15=11/15 nên 111111/151515=11022=15030
bài 22
111111/151515=11022/15030
bài 15
2004/2005 nhỏ nhất
bài 18
=1093/2187
quên nữa so sánh b với 3 nha
\(3=\frac{2006}{2007}+\frac{1}{2007}+\frac{2007}{2008}+\frac{1}{2008}+\frac{2008}{2009}+\frac{1}{2009}=B+\frac{1}{2007}+\frac{1}{2008}+\frac{1}{2009}\)
=>.........................