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29 tháng 8 2018

Ta có:

\(B=\dfrac{2009^{2010}-2}{2009^{2011}-2}\)

\(B< \dfrac{2009^{2010}-2+2011}{2009^{2011}-2+2011}\)

\(B< \dfrac{2009^{2010}+2009}{2009^{2011}+2009}\)

\(B< \dfrac{2009\left(2009^{2009}+1\right)}{2009\left(2009^{2010}+1\right)}\)

\(B< \dfrac{2009^{2009}+1}{2009^{2010}+1}\)

\(A=\dfrac{2009^{2009}+1}{2009^{2010}+1}\)

\(\Rightarrow B< A\)

12 tháng 1 2019

\(B=\frac{2009^{2010}-2}{2009^{2011}-2}< 1\)

\(\Rightarrow B=\frac{2009^{2010}-2}{2009^{2011}-2}< \frac{2009^{2010}-2+2011}{2009^{2011}-2+2011}=\frac{2009^{2010}+2009}{2009^{2011}+2009}\)\(=\frac{2009.\left(2009^{2009}+1\right)}{2009.\left(2009^{2010}+1\right)}=\frac{2009^{2009}+1}{2009^{2010}+1}\)

Suy ra : \(\frac{2009^{2010}-2}{2009^{2011}-2}< \frac{2009^{2009}+1}{2009^{2010}+1}\) hay \(B< A\)

Vậy \(A>B\)

7 tháng 7 2017

Do 2009\(^{2010}\)-2 < 2009\(^{2011}\)-2 \(\Rightarrow\)B<1

Theo đề bài ta có: 

B= \(\frac{2009^{2010}-2}{2009^{2011}-2}\)\(\frac{2009^{2010}-2+2011}{2009^{2011}-2+2011}\)\(\frac{2009^{2010}+2009}{2009^{2011}+2009}\)\(\frac{2009.\left(1+2009^{2009}\right)}{2009.\left(1+2009^{2010}\right)}\)\(\frac{2009^{2009}+1}{2009^{2010}+1}\)= A \(\Rightarrow\)B<A