Question

Prove that:
$\frac{2^n+2^{n-1}}{2^{n+1}-2^n}=\frac{3}{2}$.

Answer 1

$\frac{2^n+2^{n-1}}{2^{n+1}-2^n}$ $=\frac{2^n+2^n{.2}^{-1}}{2^n{.2}^1-2^n}$ $[a^3{a}^c=a^{b+c}]$

$\Rightarrow \frac{2^n[1+1/2]}{2^n[2-1]}$ $=1+\frac{1}{2}$ $=\frac{3}{2}$ Hence proved