Let $f_{n}\left( x\right) =\dfrac {x^{n}} {1+x^{n}},x\in \left[ 0,2\right]$
Does $f_{n}$ converge uniformly?
I know that $f_{n}$ converges pointwise to $0$ for $x\in \left[ 0,1\right)$, $1/2$ for $x=1$, and $1$ for $x\in \left(1,2\right]$, but I need help showing if it converges uniformly or not. Thanks!