Ok, I chose to ask about ways to determine if a series of functions is NOT uniformly convergent because I think that would best answer the overall difficulties I have with uniform convergence. I have a good idea of what uniform convergence is, I can give the definition, and if the problem is...
I am having a very similar problem, but for the general case of
\sum \sin( \frac{x}{n^2})
. I cannot think of a proper comparison for this. I'm not sure if the inequality stated above still holds.