Question

Prove :::: 2^n + 2^(n - 1) / 2 ^(n+1)-2^n = 3 /2

Answer 1

$Given : \frac{2^n + 2^{n - 1} }{ 2^{n + 1} - 2^n }$

$= \ \textgreater \ \frac{2^n + 2^n * 2^{-1} }{2^n * 2 - 2^n}$

$= \ \textgreater \ \frac{2^n + 2^n * \frac{1}{2} }{2^n(2 - 1)}$

$= \ \textgreater \ \frac{2^n + \frac{2^n}{2} }{2^n(2 - 1)}$

$= \ \textgreater \ \frac{2^n(1 + \frac{1}{2} )}{2^n(2 - 1)}$

$= \ \textgreater \ \frac{ \frac{3}{2} }{1}$

= > 3/2.


Hope this helps!