Sửa đề:
So sánh:
\(A=\dfrac{10^{2015}+1}{10^{2016}+1}\) và \(B=\dfrac{10^{2016}+1}{10^{2017}+1}\)
Giải:
Ta thấy: \(\left\{{}\begin{matrix}A=\dfrac{10^{2015}+1}{10^{2016}+1}< 1\\B=\dfrac{10^{2016}+1}{10^{2017}+1}< 1\end{matrix}\right.\)
\(\Rightarrow\) Áp dụng tính chất \(\dfrac{a}{b}< 1\Rightarrow\dfrac{a}{b}< \dfrac{a+m}{b+m}\) ta có:
\(B=\dfrac{10^{2016}+1}{10^{2017}+1}< \dfrac{10^{2016}+1+9}{10^{2017}+1+9}=\dfrac{10^{2016}+10}{10^{2017}+10}\)
\(=\dfrac{10\left(10^{2015}+1\right)}{10\left(10^{2016}+1\right)}=\dfrac{10^{2015}+1}{10^{2016}+1}\)
\(\Rightarrow\dfrac{10^{2016}+1}{10^{2017}+1}< \dfrac{10^{2015}+1}{10^{2016}+1}\)
Vậy \(B< A\)
Hay \(A>B\)
