Convergence of $\sum_{n=2}^{\infty} \frac{1}{n^{p} \ln(n)^{2}}$ for $p>0$
On convergence of Bertrand series $\sum\limits_{n=2}^{\infty} \frac{1}{n^{\alpha}\ln^{\beta}(n)}$ where $\alpha, \beta \in \mathbb{R}$