Hi,

Show that the series $\displaystyle \sum \frac{x^n}{1+x^n}$ converges uniformly on [0,a] for any a in (0,1)

There is a theorem in the book that says that is the series of functions satisfies the cauchy criterion uniformly on a set S, then the series converges uniformly on S. So I guess i'm supposed to use that. I'm not sure how to do a cauchy criterion proof though.

Thanks