so sanh A va B
A =\(\frac{2009}{2010}\) +\(\frac{2010}{2011}\) B =\(\frac{2009+2010}{2010+2011}\)
Những câu hỏi liên quan
17 tháng 8 2018 lúc 19:16
So sánh : \(A=\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}vàB=\frac{2008+2009+2010}{2009+2010+2011}\)
So sanh : U = \(\frac{2009^{2005}+1}{2009^{2010}+1}\)va V = \(\frac{2009^{2010}+2}{2009^{2011}+2}\)
So sánh A và B biết
A=\(\frac{2009}{2010}+\frac{2010}{2011}+\frac{2011}{2012}\)
B=\(\frac{2009+2010+2011}{2010+2011+2012}\)
A=2.998508205
B=0.999502735
suy ra A>B
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Bài giải
Theo bài ra :
\(A=\frac{2009}{2010}+\frac{2010}{2011}+\frac{2011}{2012}\)
\(B=\frac{2009+2010+2011}{2010+2011+2012}=\frac{2009}{2010+2011+2012}+\frac{2010}{2010+2011+2012}+\frac{2011}{2010+2011+2012}\)
Ta có :
\(\frac{2009}{2010}>\frac{2009}{2010+2011+2012}\)
\(\frac{2010}{2011}>\frac{2010}{2010+2011+2012}\)
\(\frac{2011}{2012}>\frac{2011}{2010+2011+2012}\)
\(\Rightarrow\text{ }\frac{2009}{2010}+\frac{2010}{2011}+\frac{2011}{2012}>\frac{2009}{2010+2011+2012}+\frac{2010}{2010+2011+2012}+\frac{2011}{2010+2011+2012}\)
\(\Rightarrow\text{ }A>B\)
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Bài giải
Theo bài ra :
\(A=\frac{2009}{2010}+\frac{2010}{2011}+\frac{2011}{2012}\)
\(B=\frac{2009+2010+2011}{2010+2011+2012}=\frac{2009}{2010+2011+2012}+\frac{2010}{2010+2011+2012}+\frac{2011}{2010+2011+2012}\)
Ta có :
\(\frac{2009}{2010}>\frac{2009}{2010+2011+2012}\)
\(\frac{2010}{2011}>\frac{2010}{2010+2011+2012}\)
\(\frac{2011}{2012}>\frac{2011}{2010+2011+2012}\)
\(\Rightarrow\text{ }\frac{2009}{2010}+\frac{2010}{2011}+\frac{2011}{2012}>\frac{2009}{2010+2011+2012}+\frac{2010}{2010+2011+2012}+\frac{2011}{2010+2011+2012}\)
\(\Rightarrow\text{ }A>B\)
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Xem thêm câu trả lời
So sánh : A=\(\frac{2008}{2009}\)+\(\frac{2009}{2010}\)+\(\frac{2010}{2011}\)và B=\(\frac{2008+2009+2010}{2009+2010+2011}\)
\(B=\frac{2008+2009+2010}{2009+2010+2011}\)
\(=\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{2010}{2009+2010+2011}\)
\(< \frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}=A\)
\(B=\frac{2008+2009+2010}{2009+2010+2011}\)
\(=\frac{2008}{2009+2010+2011}=\frac{2009}{2009+2010+2011}=\frac{2010}{2009+2010+2011}\)
\(< A=\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}\)
Cho \(\frac{2010\cdot c-2011\cdot b}{2009}=\frac{2011\cdot a-2009\cdot c}{2010}=\frac{2009\cdot b-2010\cdot c}{2011}\)
C/m \(\frac{a}{2009}=\frac{b}{2010}=\frac{c}{2011}\)
so sanh
a)-22/45 va -51/101
b)so sanh A=\(\frac{^{2009^{2009}}+1}{^{2009^{20010}}+1}\)va B=\(\frac{2009^{2010}-2}{2009^{2011}-2}\)
câu a ta so sánh số đối của 2 phân số này.nếu ps nào có giá trị tuyệt đối lớn hơn thì nhỏ hơn.
câu b ta nhân cả A và B với 2009 rồi so sánh 2009A với 2009B.ta được A>B
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Cho số A=2011; b khác 2009; c khác 2010 và \(\frac{a-2009}{b-2011}=\frac{b-2011}{c-2010}:\frac{2011-b}{2010-c}=\frac{2010-c}{2009-a}\)
Tìm tỉ số \(\frac{b}{c}\)?
\(\frac{b-2011}{c-2010}:\frac{2011-b}{2010-c}=\frac{b-2011}{c-2010}\cdot\frac{-\left(c-2010\right)}{-\left(b-2011\right)}=1\)
\(\frac{a-2009}{b-2011}=\frac{2010-c}{2009-a}=\frac{-\left(c-2010\right)}{-\left(a-2009\right)}=\frac{c-2010}{a-2009}=1\Rightarrow a-2009=c-2010=b-2011\)
\(\Rightarrow a=c-1=b-2\Rightarrow c=b-1\Rightarrow\frac{b}{c}=\frac{b}{b-1}\)=.=' ko chắc lăm
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Thanks!!! Nhưng xin lỗi mặc dù phải là -1. Cảm ơn bạn
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Xem thêm câu trả lời
so sanh
A=2008/2009+2009/2010+2010+2011
B=2008+2009+2010/2009+2010+2011
Dễ thấy:
\(\frac{2008}{2009}>\frac{2008}{2009+2010+2011}\)
\(\frac{2009}{2010}>\frac{2009}{2009+2010+2011}\)
\(\frac{2010}{2011}>\frac{2010}{2009+2010+2011}\)
=>\(\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}>\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{2010}{2009+2010+2011}\)
Hay \(\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}>\frac{2008+2009+2010}{2009+2010+2011}\)
Vậy A > B
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\(B=\frac{\frac{2008}{2011}+\frac{2009}{2010}+\frac{2010}{2009}+\frac{2011}{2008}+\frac{2012}{503}}{\frac{1}{2008}+\frac{1}{2009}+\frac{1}{2010}+\frac{1}{2011}}\)