The discussion revolves around determining the convergence of the series involving the term ln(n)/(ln(ln(n))) for n starting from 3 to infinity. Participants express uncertainty about the appropriate comparison series to use for applying the limit test.
Participants are actively exploring different methods to assess the convergence of the series. Some have suggested using the nth term test for divergence based on observations about the growth rates of the logarithmic functions involved. There is no explicit consensus yet, but several lines of reasoning are being examined.
Participants note that the tail of the series does not seem to approach zero, which raises questions about the validity of the series' convergence. There is also mention of the need to justify comparisons made in the limit test.
Sure, you can use 1/n in the limit comparison test.MozAngeles said:Homework Statement
Sum ln n/(ln(ln n)) n=3..infinity?
Im pretty sure it diverges and I am pretty sure to use the limit test but i just don't know what to compare this sum to. Would 1/n be ok. Do i have to justify why they are similar?
ANy help would be nice thanks.
Char. Limit said:You could also just see that log(n) is larger than log(log(n)) for basically every n you're using, and so you're summing a sequence of numbers that all are greater than 1. So realistically, you could use a limit comparison with 1.
wisvuze said:even worse, the tail of this series doesn't seem to go to 0, log(x) will grow faster than log(log(x))