Prove that $\sum x^n$ does not uniformly converge for $x \in [0,1)$

I am trying to prove this by showing that $\lim_n \sup \{f - f_n : x \in [0,1)\} \neq 0$. I find that $f - f_n = \frac{x^n}{1-x}$. How can I show that the limsup of $\frac{x^n}{1-x}$ is not equal to 0?