Uniform convergence of the power series on $\mathbb R^-$

Question

I need to determine whether the power series $$ \sum _{n=2}^{\infty} \frac{x^{n}}{\ln \left(n\right)}\quad x\in \Bbb{R} , $$ converges uniformly or not on the interval $[-1,0]$. I know already that the power series has a radius of convergence $R=1$, and I do also know that the primitive of the power series is continuous in $-R=-1$, i.e. the primitive is continuous on $[-1,1)$.

Answer 1

If you could show convergence at $x=-1$,then abel's theorem will guarantee that it converges uniformly on $[-1,0]$.