X=?

$\displaystyle \begin{aligned} 1 + x + x^2 + x^3 + x^4 + \cdots & = 2017 \\ \implies 1 + x(1 + x + x^2 + x^3 + \cdots) & = 2017 \\ \implies 1 + 2017x & = 2017 \\ \implies x & = \boxed{\displaystyle \frac {2016}{2017}} \end{aligned}$

$1+x+x^2+x^3+x^4+\dots = \frac{1}{1-x} = 2017$ geometric series with ratio $x$ and infinite sum.

$\implies x=\frac{2016}{2017}$ .

Another solution: the above expression is $x +x^2+x^3+\dots =2017-1=2016$

$x(1+2016)=2016 \implies x= \frac{2016}{2017}$