Đặt A=\(\frac{10^{2006}+1}{10^{2007}+1}\);\(B=\frac{10^{2007}+1}{10^{2008}+1}\)
10A=\(\frac{10\left(10^{2006}+1\right)}{10^{2007}+1}\)=\(\frac{10^{2007}+1+9}{10^{2007}+1}\)
10B=\(\frac{10\left(10^{2007}+1\right)}{10^{2008}+1}=\frac{10^{2008}+1+9}{10^{2008}+1}\)
Vì \(\frac{9}{10^{2007}+1}>\frac{9}{10^{2008}+1}\)nên 10A>10B nên A>B