Nhân a và b với 2005 ta có : 2005.a =\(\frac{2005.\left(2005^{2005}+1\right)}{2005^{2006}+1}\)=\(\frac{2005^{2006}+2005}{2005^{2006}+1}\)= \(\frac{\left(2005^{2006}+1\right)+2004}{2005^{2006}+1}\)= \(\frac{2005^{2006}+1}{2005^{2006}+1}\)+ \(\frac{2004}{2005^{2006}+1}\)=1+\(\frac{2004}{2005^{2006}+1}\) 2005.b = \(\frac{2005.\left(2005^{2004}+1\right)}{2005^{2005}+1}\)=\(\frac{2005^{2005}+2005}{2005^{2005}+1}\)= \(\frac{\left(2005^{2005}+1\right)+2004}{2005^{2005}+1}\)=\(\frac{2005^{2005}+1}{2005^{2005}+1}\)+ \(\frac{2004}{2005^{2005}+1}\) =1+\(\frac{2004}{2005^{2005}+1}\) Vì 2004=2004 , 2005^2005 +1 < 2005^2006 + 1 => \(\frac{2004}{2005^{2006}+1}\)< \(\frac{2004}{2005^{2005}+1}\)=> a<b Vậy A < B
B=(2005(2005^2004+1))/(2005(2005^2005+1))=(2005^2005+2005)/(2005^2006+2005)
Có 1-A=(2005^2006-2005^2005)/(2005^2006+1)
1-B=(2005^2006-2005^2005)/(2005^2006+2005)
suy ra 1-A>1-B.Suy ra A <B
