Đặt :
\(A=\dfrac{10^{2017}+1}{10^{2016}+1}\)
\(B=\dfrac{10^{2018}+1}{10^{2017}+1}\)
Ta thấy :
\(\left\{{}\begin{matrix}A=\dfrac{10^{2017}+1}{10^{2016}+1}>1\\B=\dfrac{10^{2018}+1}{10^{2017}+1}>1\end{matrix}\right.\)
Áp dung tính chất \(\dfrac{a}{b}>1\Leftrightarrow\dfrac{a}{b}>\dfrac{a+m}{b+m}\)
\(B=\dfrac{10^{2018}+1}{10^{2017}+1}>\dfrac{10^{2018}+1+9}{10^{2017}+1+9}=\dfrac{10^{2018}+10}{10^{2017}+10}=\dfrac{10\left(10^{2017}+1\right)}{10\left(10^{2016}+1\right)}=\dfrac{10^{2017}+1}{10^{2016}+1}=A\) \(\Leftrightarrow B>A\)
Vậy ......................
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