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 \(n\)?

\[\frac 16\] \[\frac 34\] \[\frac 13\] \[\frac 14\] \[\frac 18\] \[\frac 23\] \[\frac 15\] \[\frac 38\]

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