$\displaystyle \sum_{k=2}^\infty \frac{4}{k ln k}$
should I turn the ln into an e? What rule should I use??
Let $\displaystyle a_k=\frac{4}{k\ln(k)}$. Consider that $\displaystyle \forall{k}\in[2,\infty)~a_k>0\wedge{a_k}\in\mathcal{C}\wedge{a_k }\in\downarrow$ so the integral test applies. So this series shares convergence/divergence with $\displaystyle \int_2^{\infty}\frac{dx}{x\ln(x)}$