Leonhard Euler gave the following expression for $$ :

$\frac{}{2}=1+\frac{1}{3}(1+\frac{2}{5}(1+\frac{3}{7}(1+\frac{4}{9}(1+$cdots$))))$

Write a function which computes the first $n$ terms of this series, and use it to confirm that the $50$ th digit in the decimal expansion for $$ is $0.$