Question

How would I prove 2/2^n = 1/2^n-1

Answer 1

\[\begin{align*}\frac{2}{2^n}&=\frac{1}{2^{n-1}}\\
\frac{2^1}{2^n}&=\cdots\\
2^{1-n}&=\cdots\\
\frac{1}{2^{-(1-n)}}&=\cdots\\
\frac{1}{2^{n-1}}&=\cdots
\end{align*}\]

Answer 2

or in other words...you reduce the fraction by a factor of 2
just like 2/4 = 1/2