The slow crawl

$\sum_{n=3}^{\infty}\frac{1}{n \ln(n) \ln(\ln(n))} \geq \int_{3}^{\infty}\frac{1}{x \ln(x) \ln(\ln(x))} dx = [\ln(\ln (\ln (x)))]_{3}^{\infty}=\infty$ Hence the series diverges.

https://en.wikipedia.org/wiki/Cauchy condensation test
See this for more info about the cauchy condensation test And watch this video for more info about the limit comparison test : - https://www.youtube.com/watch?v=19bXWl9mqho