Answer
$\dfrac{257}{999}$
Work Step by Step
The general formula to find the sum of an infinite Geometric series is given as:
$ S_{n}=\dfrac{a_1}{(1-r)}$
$0.\overline{257}=\dfrac{257}{1000}+\dfrac{257}{1000000}+\dfrac{257}{1000000000}+......$
Now, $ S_{n}=\dfrac{a_1}{(1-r)}=\dfrac{257/10}{1-\dfrac{1}{1000}}$
Our answer is: $ S_{n}=\dfrac{257/10}{999/1000}=\dfrac{257}{999}$
