Question

Is the series Σ(1/log(n)) , for n=2 -> infinity convergent and if yes how to prove it?

Answer 1

definitely not convergent

Answer 2

for one thing \(\ln(n)<n\) making \(\frac{1}{\ln(n)}>\frac{1}{n}\) so comparison test will give you a quick answer, but by eyeballing it you can tell it does not converge because log grows very slowly

Answer 3

Thanks!