Answer
$\dfrac{257}{999}$
Work Step by Step
Sum of the first $n$ terms terms of a geometric sequence can be calculated as: $s_n=\dfrac{a_1}{(1-r)}$
$r$ refers to common ratio and $r=\dfrac{1}{1000}=0.01$ and $S_n=0.\overline{257}$
Apply the formula.
$s_n=\dfrac{0.257}{(1-0.001)}=\dfrac{0.257}{0.999}=\dfrac{257}{999}$
