Am I right in saying that if I have $\displaystyle f_n=\frac{x^n}{x^n+1}$ and

$\displaystyle f(x) = \left\{\begin{array}{c l} 0 & x \in [0,1)\\ 0.5 & x =1 \\ 1 & x\in(1,\infty)\end{array}\right.$

definied on $\displaystyle (0,\infty)$ is not uniform convergent to f(x) (the problem being near the 1)?

Thanks for any help