Showing whether a series is convergent: sum[3,infty] [sin(1/{3 ln(n)})]/n

[oh_no]

Hi all,

I have spent the past day looking at this series:

\(\displaystyle \displaystyle \sum_3^\infty \dfrac{\sin\left(\frac{1}{3\, \ln(n)}\right)}{n}\)

I am required to show whether the series is divergent or convergent.
However, I have been unable to do so.
What I know is that wolframalpha used the comparison test to show the series diverges.

Any help would be greatly appreciated!

 

[ksdhart2]

Well, given that Wolfram Alpha uses the comparison test, that suggests to me that might be a good tactic to try. The question is, what series have you tried comparing the given series to? Are the series you chose bigger or smaller than the given? Do the series you chose diverge or converge? What, if anything, does that tell you about the given series?