Inspired by a Brilliant problem

Algebra Level 2

$\large n = \frac{1}{2^1}+\frac{1}{2^3}+\frac{1}{2^5}+\frac{1}{2^7}+\cdots$

What is $n$ ?

\frac 16

\frac 34

\frac 13

\frac 14

\frac 18

\frac 23

\frac 15

\frac 38