Hello.

I have proved that the series $\displaystyle $\sum_{n=2}^{\infty}\frac{\left (\mathrm{ln}\left ( n \right ) \right )^{p}}{n}$$ is convergent if $\displaystyle p<-1$ and divergent if $\displaystyle p\geq -1$.

So the another problem is about to show the series $\displaystyle $\sum_{n=2}^{\infty}\frac{\left (\mathrm{ln}\left ( n \right ) \right )^{x}}{n}$$ is uniform convergent as $\displaystyle $x \in ]-\infty;p]$$ if $\displaystyle p<-1$.

I am not sure what to do. If it's true that I should use the Weierstrass Test, could you please tell me what do to? Even I have read about it I feel kinda stuck when I try to answer this problem.

(I am sorry if I have posted it in the wrong place.)