Consider

$\displaystyle f (x) = \sum_{n=1} ^ {\infty} 1/{n(1 + nx^2)}$

(a) For what values of $\displaystyle x$ does the series converge?

(b) On what intervals of the form $\displaystyle (a,b)$ does the series converge uniformly?

(c) On what intervals of the form $\displaystyle (a,b)$ does the series fail to converge uniformly?

(d) Is $\displaystyle f$ continuous at all points where the series converges?

I would appreciate any help. Meanwhile I am trying to do the question by myself and would let everyone know of any breakthroughs.

Thanks