Is power series $\sum_{n=1}^\infty\frac{x^n}{n}$ uniformly convergent in $(-1,1)$

Question

I know that if $\sum a_nx^n$ has radius of convergence R then this power series converges uniformly for every compact subset of $(-R,R)$ and now no doubt converges pointwise in $(-R,R)$ but little bit confused what can we say about uniform convergence in $(-R,R)$.

As for example what can we say about uniform convergence of series $\sum_{n=1}^\infty\frac{x^n}{n}$ in (-1,1)?

Answer 1

Hint: Any partial sum is bounded, but the series converges pointwise to something unbounded.