Uniform convergence on $[0,1]$ versus $[0,\tfrac12]$

Suppose $\{f_n\}$ is defined by $f_n(x)=\dfrac{x^{n}}{1+x^{n}}$, $0\le x\le 1$. Which of the following is true?

$S_1$: $f_n\to f\equiv 0$ uniformly on $[0,1]$.
$S_2$: $\displaystyle\sup_{0\le x\le 1/2} f_n(x)\to \mathrm{F}(x)\equiv0$ on $[0,\tfrac12]$.
$S_3$: $f_n\to f= 0$ uniformly on $[0,\tfrac12]$.