Is the sequence of functions $f\_n(x) = x^n$ uniformly convergent on $[0,1)$? I learned that $f\_n(x)$ is not uniformly convergent on $[0,1]$ but what about on $[0,1)$? I think it does converge uniformly to $f(x)=0$ because I can always make $n$ big enough to fit $x^n$ to be within $\epsilon$ from $0$ for any $x$? Or is this not possible? I am not really sure on how to verify a sequence of functions is uniformly convergent on some domain. 

Also, does uniformly convergent series imply that the series is also absolutely convergent?