Name: Anonymous 2010-06-12 6:25
Hi,
I have the following series: \sum_{n=2}^{\infty}\frac{1}{n\,\textup{log}^{2}n}
I just want to know whether it converges or not. I've tried all the convergence tests I've found (at least inf limit, ratio, root, Raabe, Cauchy, maybe some other I forgot?), none is conclusive. I've tried to numerically sum it (just to get an idea), but with floating point doubles I run out of precision and with arbitrary precision arithmetic I run out of patience before reaching any conclusion.
My hunch it that it doesn't converge. It's not really important but it's been bugging me, I must have missed something obvious.
I have the following series: \sum_{n=2}^{\infty}\frac{1}{n\,\textup{log}^{2}n}
I just want to know whether it converges or not. I've tried all the convergence tests I've found (at least inf limit, ratio, root, Raabe, Cauchy, maybe some other I forgot?), none is conclusive. I've tried to numerically sum it (just to get an idea), but with floating point doubles I run out of precision and with arbitrary precision arithmetic I run out of patience before reaching any conclusion.
My hunch it that it doesn't converge. It's not really important but it's been bugging me, I must have missed something obvious.