Bài 2 : So sánh
\(A=\dfrac{2008}{2009}+\dfrac{2009}{2010}+\dfrac{2010}{2011}vàB=\dfrac{2008+2009+2010}{2009+2010+2011}\)
Những câu hỏi liên quan
Bài 2 : So sánh
\(A=\dfrac{2008}{2009}+\dfrac{2009}{2010}+\dfrac{2010}{2011}vàB=\dfrac{2008+2009+2010}{2009+2010+2011}\)
Ta có :
\(B=\frac{2008+2009+2010}{2009+2010+2011}=\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{2010}{2009+2010+2011}\)
Vì :
\(\frac{2008}{2009}>\frac{2008}{2009+2010+2011}\)
\(\frac{2009}{2010}>\frac{2009}{2009+2010+2011}\)
\(\frac{2010}{2011}>\frac{2010}{2009+2010+2011}\)
Nên \(\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}>\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{2010}{2009+2010+2011}\)
\(\Rightarrow\)\(A>B\)
Vậy \(A>B\)
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Ta có: \(B=\frac{2008+2009+2010}{2009+2010+2011}\)
\(=\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{2010}{2009+2010+2011}\)
Vì \(\frac{2008}{2009}>\frac{2008}{2009+2010+2011}\)
\(\frac{2009}{2010}>\frac{2009}{2009+2010+2011}\)
\(\frac{2010}{2011}>\frac{2010}{2009+2010+2011}\)
nên \(\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}>\frac{2008+2009+2010}{2009+2010+2011}\)
hay A > B
Vậy A > B
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So sánh A và B biết: A= \(\dfrac{2008+2008+2010}{2009+2010+2011}\) và B= \(\dfrac{2008}{2009}\)+ \(\dfrac{2009}{2010}\)+ \(\dfrac{2010}{2011}\)
A = \(\dfrac{2008}{2009+2010+2011}+\dfrac{2009}{2009+2010+2011}+\dfrac{2010}{2009+2010+2011}\)
Ta có:
\(\dfrac{2008}{2009}>\dfrac{2008}{2009+2010+2011}\)
\(\dfrac{2009}{2010}>\dfrac{2009}{2009+2010+2011}\)
\(\dfrac{2010}{2011}>\dfrac{2010}{2009+2010+2011}\)
Từ 3 điều trên suy ra : A < B
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17 tháng 8 2018 lúc 19:16
So sánh : \(A=\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}vàB=\frac{2008+2009+2010}{2009+2010+2011}\)
Bài 2 : So sánh
A=2008/2009+2009+2010+2010+2011 và B=2008+20092+2010/2009+2010+2011
So Sánh : A = \(\dfrac{2009^{2009}+1}{2009^{2010}+1}\) và B = \(\dfrac{2009^{2010}-2}{2009^{2011}-2}\)
Ta có :
\(B=\dfrac{2009^{2010}-2}{2009^{2011}-2}< 1\)
\(\Leftrightarrow B< \dfrac{2009^{2010}-2+2011}{2009^{2011}-2+2011}=\dfrac{2009^{2010}+2009}{2009^{2011}+2009}=\dfrac{2009\left(2009^{2009}+1\right)}{2009\left(2009^{2010}+1\right)}=\dfrac{2009^{2009}+1}{2009^{2010}+1}=A\)
\(\Leftrightarrow A>B\)
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\(A=\dfrac{5^{2011}-5^{2010}+5^{2009}-5^{2008}+....+5-1}{5^{2013}-5^{2012}+5^{2011}-5^{2010}+....+5-1}\) \(B=\dfrac{5^{2009}-5^{2008}+5^{2007}-5^{2006}+....+5-1}{5^{2011}-5^{2010}+5^{2009}-5^{2008}+....+5-1}\)
So sánh A và B
so sánh A và B với A=2008/2009 +2009/2010 +2010/2011 và B= (2008+2009+2010) / (2009+2010+2011)
mình cũng có bài giống như này nhưng chưa làm được
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Ta có: 2008/2009 > 2008/2009+2010+2011
2009/2010> 2009/2010+2011
2010/2011>2010>2010/2009+2010+2011
Suy ra: A>2008+2009+2010/2009+2010+2011
Vậy A >B
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so sánh A và B với A=2008/2009 +2009/2010 +2010/2011 và B= 2008+2009+2010 / 2009+2010+2011
Tớ cũng có bài này nhưng chưa làm được
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cau tra loi la 50 khong can biet lam the nao
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BT1: Tính
5) \(\dfrac{1}{1+\dfrac{2009}{2011}+\dfrac{2009}{2010}}+\dfrac{1}{1+\dfrac{2010}{2009}+\dfrac{2010}{2011}}+\dfrac{1}{1+\dfrac{2011}{2009}+\dfrac{2011}{2010}}\)
=\(\dfrac{1}{2009.\left(\dfrac{1}{2009}+\dfrac{1}{2011}+\dfrac{1}{2010}\right)}+\dfrac{1}{2010.\left(\dfrac{1}{2010}+\dfrac{1}{2009}+\dfrac{1}{2011}\right)}+\dfrac{1}{2011.\left(\dfrac{1}{2011}+\dfrac{1}{2009}+\dfrac{1}{2010}\right)}\)\(=\dfrac{1}{2009}:\left(\dfrac{1}{2009}+\dfrac{1}{2010}+\dfrac{1}{2011}\right)+\dfrac{1}{2010}:\left(\dfrac{1}{2009}+\dfrac{1}{2010}+\dfrac{1}{2011}\right)+\dfrac{1}{2011}:\left(\dfrac{1}{2009}+\dfrac{1}{2010}+\dfrac{1}{2011}\right)\)
\(=\left(\dfrac{1}{2009}+\dfrac{1}{2010}+\dfrac{1}{2011}\right):\left(\dfrac{1}{2009}+\dfrac{1}{2010}+\dfrac{1}{2011}\right)=1\)
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