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

Áp dụng \(\frac{a}{b}< 1\Leftrightarrow\frac{a}{b}< \frac{a+m}{b+m}\)(\(a;b;m\in\)N*)

Ta có: 

\(B=\frac{10^{2007}+1}{10^{2008}+1}< \frac{10^{2007}+1+9}{10^{2008}+1+9}\)

\(B< \frac{10^{2007}+10}{10^{2008}+10}\)

\(B< \frac{10.\left(10^{2006}+1\right)}{10.\left(10^{2007}+1\right)}\)

\(B< \frac{10^{2006}+1}{10^{2007}+1}=A\)

=> \(B< A\)

thank you

ta thay : 1- 2005/2006 = 1/2006 ; 1 - 2006/2007 = 1/2007

vi 1/2006 > 1/2007 nen 2005/2006 < 2006/2007

bai nay dung 100 % . bai la phuong phap phan bu , ban co the lam phuong phap phan so trung gian , quy dong tu so hoac  mau so

\(1-\frac{2005}{2006}=\frac{1}{2006};1-\frac{2006}{2007}=\frac{1}{2007}\)

Vì \(\frac{1}{2006}>\frac{1}{2007}\Rightarrow\frac{2005}{2006}< \frac{2006}{2007}\)

vì \(\frac{10^{2006}+1}{10^{2007}+1}\)<1

tc:B=\(\frac{10^{2006}+1}{10^{2007}+1}\)<\(\frac{10^{2006}+1+9}{10^{2007}+1+9}\)=\(\frac{10^{2006}+10}{10^{2007}+10}\)=\(\frac{10\left(10^{2005}+1\right)}{10\left(10^{2006}+1\right)}\)=\(\frac{10^{2005}+1}{10^{2006}+1}\)=A

=>B<A

A<B

quy tắc:  a/b <1 thì a/b<a+m/b+m

a/b>1 thì a/b> a+m/b+m

em có thể gõ lại công thức đc k