Question

SS

A = \(\dfrac{2009^{2008}+1}{2009^{2009}+1}\) và B = \(\dfrac{2009^{2009}+1}{2009^{2010}+1}\)

Answer 1

B = \(\dfrac{2009^{2009}+1}{2009^{2010}+1}\)<\(\dfrac{2009^{2009}+1+2008}{2009^{2010}+1+2008}\)=\(\dfrac{2009^{2009}+2009}{2009^{2010}+2009}\)=\(\dfrac{2009.\left(2009^{2008}+1\right)}{2009.\left(2009^{2009}+1\right)}\)=\(\dfrac{2009^{2008}+1}{2009^{2019}+1}\)= A

Vậy A > B

Answer 2

Ta có :

\(2009A=\dfrac{2009^{2009}+2009}{2009^{2009}+1}=\dfrac{2009^{2009}+1+2008}{2009^{2009}+1}=\dfrac{2009^{2009}+1}{2009^{2009}+1}+\dfrac{2008}{2009^{2009}+1}=1+\dfrac{2008}{2009^{2009}+1}\)

\(2009B=\dfrac{2009^{2010}+2009}{2009^{2010}+1}=\dfrac{2009^{2010}+1+2008}{2010^{2010}+1}=\dfrac{2009^{2010}+1}{2009^{2010}+1}+\dfrac{2008}{2009^{2010}+1}=1+\dfrac{2008}{2009^{2010}}\)

\(\)Vì \(1+\dfrac{2008}{2009^{2009}+1}>1+\dfrac{2008}{2009^{2010}+1}\Rightarrow A>B\)

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