Question

Cho A = \(\dfrac{10^{2006}+1}{10^{2007}+1}\)

B= \(\dfrac{10^{2007}+1}{10^{2008}+1}\)

So sánh A và B

Answer 1

Áp dụng bất đẳng thức :

\(\dfrac{a}{b}< 1\Leftrightarrow\dfrac{a}{b}< \dfrac{a+m}{b+m}\left(a;b;m\in N;b\ne0\right)\)

Ta có : \(B=\dfrac{10^{2007}+1}{10^{2008}+1}< 1\)

\(\Leftrightarrow B=\dfrac{10^{2007}+1}{10^{2008}+1}< \dfrac{10^{2007}+1+9}{10^{2008}+1+9}=\dfrac{10^{2007}+10}{10^{2008}+10}=\dfrac{10\left(10^{2006}+1\right)}{10\left(10^{2007}+1\right)}=\dfrac{10^{2006}+1}{10^{2007}+1}=A\)

\(\Leftrightarrow B< A\)