Prove: \[ \frac{2^n + 2^{n-1}}{2^{n+1} – 2^n} = \frac{3}{2} \]
Proof
\[ = \frac{2^n + 2^{n-1}}{2^{n+1} – 2^n} \]
\[ = \frac{2^{n-1}(2 + 1)}{2^n(2 – 1)} \]
\[ = \frac{2^{n-1} \cdot 3}{2^n \cdot 1} \]
\[ = \frac{3}{2} \]
\[ = \frac{2^n + 2^{n-1}}{2^{n+1} – 2^n} \]
\[ = \frac{2^{n-1}(2 + 1)}{2^n(2 – 1)} \]
\[ = \frac{2^{n-1} \cdot 3}{2^n \cdot 1} \]
\[ = \frac{3}{2} \]