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\(B=\frac{2008+2009+2010}{2009+2010+2011}\)
\(=\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{2010}{2009+2010+2011}\)
\(< \frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}=A\)
1.
\(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{99}}+\frac{1}{2^{100}}+\frac{1}{2^{100}}\)
\(=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{99}}+\left(\frac{1}{2^{100}}+\frac{1}{2^{100}}\right)\)
\(=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{99}}+\frac{1}{2^{99}}\)
cứ làm như vậy ta được :
\(=1+1=2\)
2. Ta có :
\(\frac{2008+2009}{2009+2010}=\frac{2008}{2009+2010}+\frac{2009}{2009+2010}\)
vì \(\frac{2008}{2009}>\frac{2008}{2009+2010}\); \(\frac{2009}{2010}>\frac{2009}{2009+2010}\)
\(\Rightarrow\frac{2008}{2009}+\frac{2009}{2010}>\frac{2008+2009}{2009+2010}\)
Ta có :
\(B=\frac{2008+2009+2010}{2009+2010+2011}=\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{20101}{2009+2010+2011}\)
Ta thấy \(\frac{2008}{2009}>\frac{2008}{2009+2010+2011}\); \(\frac{2009}{2010}>\frac{2009}{2009+2010+2011}\);
\(\frac{2010}{2011}>\frac{2010}{2009+2010+2011}\)
Suy ra : A > B
B = 20092009 + 1 / 20092010+1 < 20092009+1+2008 / 20092010+1+2008
= 20092009+2009 / 20092010+2009
= 2009(20092008+1) / 2009(20092009+1)
= 20092008+1 / 20092009+1 = A
=> A > B nhé!
Ai k mk mk k lại !!
bạn c/m bài toán \(\frac{a}{b}<1;a,b>0\Rightarrow\frac{a+c}{b+c}>\frac{a}{b}\)
Trả lời
2009.2011+2010/2008.2012+2009 lớn hơn 1.
Học tốt !
trinh bay ra duoc khong