Question

So sánh:\(\dfrac{10^{2011}+1}{10^{2012}+1}và\dfrac{10^{2010}+1}{10^{2011}+1}\)

Answer 1

a/ Áp dụng bất đẳng thức :

\(\dfrac{a}{b}< 1\Leftrightarrow\dfrac{a}{b}< \dfrac{a+m}{b+m}\)

Ta có :

\(\dfrac{10^{2011}+1}{10^{2012}+1}< 1\)

\(\Leftrightarrow\dfrac{10^{2011}+1}{10^{2012}+1}< \dfrac{10^{2011}+1+9}{10^{2012}+1+9}=\dfrac{10^{2011}+10}{10^{2012}+10}=\dfrac{10\left(10^{2010}+1\right)}{10\left(10^{2011}+1\right)}=\dfrac{10^{2010}+1}{10^{2011}+1}\)

\(\Leftrightarrow\dfrac{10^{2011}+1}{10^{2012}+1}< \dfrac{10^{2010}+1}{10^{2011}+1}\)