Help finding the behaviour of this series?

  • Thread starter Dell
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  • #1
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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

  • #2
king vitamin
Science Advisor
Gold Member
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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.
 

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