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))
A series is a mathematical expression that consists of a sequence of terms added together. Convergence refers to the behavior of a series and whether the sum of its terms approaches a finite value or not.
A series is said to converge if the sum of its terms approaches a finite value as the number of terms increases. In other words, the series has a well-defined finite limit.
There are several tests that can be used to determine the convergence of a series, such as the ratio test, the comparison test, and the integral test. These tests involve analyzing the behavior of the terms in the series and can help determine if the series converges or diverges.
Absolute convergence occurs when the series converges regardless of the order in which its terms are added. On the other hand, conditional convergence occurs when the series only converges if its terms are added in a specific order.
If a series does not converge, it is said to diverge. This means that the sum of its terms does not approach a finite value and the behavior of the series is unpredictable. Divergent series can still have useful properties and applications, but they do not have a well-defined finite limit.