Is the series of sin(nx)/n^2 continuous on R?

[Rosey24]

Homework Statement

Show that \Sigma (from n=1 to infinity) of sin(nx)/n^2
is continuous on R

Homework Equations

The Attempt at a Solution

No idea, any help would be greatly appreciated.

 

[Mystic998]

Well, that would depend on what you're allowed to use. But uniform convergence of the series pretty much implies it immediately. And showing uniform convergence is easy.

Otherwise, I imagine it's a bit trickier, and I'd have to think about it.

 

[Rosey24]

I am allowed to use uniform convergence. Thanks!