Which of the following sequences of functions $\left \{ f_{n} \right \}_{n=1}^{\infty }$ converges uniformly ?
- $f_{n}\left ( x \right )=x^{n}\:on \: \left [ 0,1 \right ]$
- $f_{n}\left ( x \right )=1-x^{n} \:on\: \left [ \frac{1}{2},1 \right ]$
- $f_{n}\left ( x \right )=\frac{1}{1+nx^{2}}\:on\: \left [ 0,\frac{1}{2} \right ]$
- $f_{n}\left ( x \right )=\frac{1}{1+nx^{2}}\:on\: \left [ \frac{1}{2},1 \right ]$
