Q:

Prove the existence of an $n'$ such as for all $n>n'$ : $\frac{U_{n+1}}{U_n} < 3/4$

Let $U_n$ be a numerical sequence defined by $U_n=n^2/2^n$
We need to deduce from the fact that the limit of $U_{n+1}/U_n$ equals $1/2$ the existence of $n'.$
How am I supposed to prove its existence. It's clear that next to $+\infty$ this condition is valid ; Am I right? 

A:

Hint In the definition of limit use $\epsilon =\frac{1}{4}$.

