\lim_{n\to \infty } \frac{\left(1+\frac{1}{2n}\right)}{\left(1-\frac{1}{2n}\right)}=\frac{\left(1+\frac{1}{2\infty}\right)}{(1-\frac{1}{2\infty})}=\frac{(1+0)}{(1-0)}=\frac{1}{1}=1