Let $f_{n}\left( x\right) =\dfrac {x^{n}} {1+x^{n}}$, $x \in \left[ 0,2\right]$
Show that $f_{n}$ converges pointwise on $[0,2]$.
I know that the function converges to $0$ for $0\leq x < 1$, converges to $1/2$ for $x=1$ and converges to $1$ for $x>1$, but I need help showing the definition of pointwise convergence given $\varepsilon>0$.
Thanks!