# Help finding the behaviour of this series?

given the following series and i am asked if it converges or diverges in its boundaries

0 + ln(2)/4 + ln(3)/9 + ln(4)/16 + ...... + ln(n)/n^2

to find out if series converge/diverge, i have been using comparisons, finding a similar series, B(n) whose behaviour i know or can easily find, then saying :
# if B(n) > A(n), and B(n) converges, then A(n) converges
# if B(n) < A(n), and B(n) diverges, then A(n) diverges
# if A(n)/B(n)=K (K= not 0, not ∞) then A(n) and B(n) behave the same

but i cannot find any series that answers to any of these 3 condidtions, any ideas? the series must either have a known or relatively simple to find behaviour.

## Answers and Replies

king vitamin
Science Advisor
Gold Member
Finding the convergence of series involving logs can be tough because it can be hard to see how log behaves in comparison to polynomials. To get a good sense of this, try graphing in the same window y=ln(x) along with some polynomials such as y=x, y=x^(1/2), y=x^(1/5), etc. What you should generally find is that all x^a (with a > 0) is less than ln(x) for large x. This should help you find a convergent polynomial series greater than yours.