[tex]\it x\cdot(1-\dfrac{1}{2})\cdot(1-\dfrac{1}{3})\cdot(1-\dfrac{1}{4})\cdot\ ...\ \cdot(1-\dfrac{1}{2016})\cdot(1-\dfrac{1}{2017})=\dfrac{1}{2018} \Rightarrow\\ \\ \\ \Rightarrow\ x\cdot\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot\ ...\ \cdot\dfrac{2015}{2016}\cdot\dfrac{2016}{2017}=\dfrac{1}{2018} \Rightarrow\ x\cdot\dfrac{1}{2017}=\dfrac{1}{2018}|_{\cdot2017}\Rightarrow\\ \\ \\ \Rightrarrow\ x=\dfrac{2017}{2018}[/tex]
