Hi! I would like to proof that converges. I already have that
or equivalently
I have also calculated the difference but i do not know how to use my inequations.
Could somebody please help me with this?
I may be wrong, but I feel like your inequality is useless: the lower bound tends to 1/2, while the upper bound diverges to (because of the last log).
However, if you know series, here's a way: find an asymptotic equivalence for in order to show that converges. Try to see why this is enough.
Thank you for the answer.
Exactly that was my problem! In order to proof that converges i was given the hint to use and the inequations . Do you know how i could use this somehow?
I do not really know how to work out your idea but i will think about it. Again i am thankful for every answer.