Ta có:
\(2007A=\dfrac{2007^{2009}+2007}{2007^{2009}+1}=1+\dfrac{2006}{2007^{2009}+1}\)\(2007B=\dfrac{2007^{2010}+10}{2007^{2010}+1}=1+\dfrac{9}{2007^{2010}+1}\)Vì \(\dfrac{2007}{2007^{2009}+1}>\dfrac{2007}{2007^{2010}+1}\)
=>2007A > 2007B
Do đó A>B
Vậy A>B
Ta có : \(B\) = \(\dfrac{2007^{2009}+1}{2007^{2010}+1}\) \(< 1\) \(\Rightarrow\dfrac{2007^{2009}+1}{2007^{2010}+1}< \dfrac{2007^{2009}+1+2006}{2007^{2010}+1+2006}\) \(=\dfrac{2007^{2009}+2007}{2007^{2010}+2007}\)
\(=\dfrac{2007\left(2007^{2008}+1\right)}{2007\left(2007^{2009}+1\right)}\) \(=\dfrac{2007^{2008}+1}{2007^{2009}+1}=A\)
Vậy \(A>B\)
\(A=\dfrac{2007^{2008}+1}{2007^{2009}+1}=\dfrac{2007^{2008}+1}{2007\cdot2007^{2008}+1}=\dfrac{1}{2007}\)
\(B=\dfrac{2007^{2009}+1}{2007\cdot2007^{2009}+1}=\dfrac{1}{2007}\)
Vậy A=B.
Ta có:
\(\dfrac{2007^{2009}}{2007^{2010}}< 1\)
Vì \(\dfrac{2007^{2009}+1}{2007^{2010}+1}< \dfrac{2007^{2009}+1+2006}{2007^{2010}+1+2006}\) \(=\dfrac{2007^{2009}+2007}{2007^{2010}+2007}=\dfrac{2007.\left(2007^{2008}+1\right)}{2007.\left(2007^{2009}+1\right)}=A\)
