Series of functions & uniform convergence

http://sites.google.com/site/asdfasdf23135/ra26.JPG

OK, so the answer I got for part a is:

S(x) = / [1- 1/(1+ )] = if x≠0

S(x) = 0 if x=0

Can someone help me with the part b, please? In general, I am having a lot of headaches on problems about uniform convergence. I know the precise definition of it, and I re-read the definition many times, but I have no idea how to actually APPLY the definition to solve actual problems.

Should we use the Weierstrass M-test here? Is this the only way to prove that a SERIES of functions is uniformly convergent?

Thanks for any help!!

[also under discussion in math link forum]