Again, the series is $$\sum_{n=1}^{\infty} \frac {(-1)^n \sin^2(8n)}{n}.$$
Wolfy says it converges, at first I thought it would converge, but after thought I think it diverges, mathway says it diverges. Regardless, I can't find a proof for either.
My highschool friends were given this assignment on a test and their teacher couldn't show the answer either way. I looked at it and thought that because the sin term is always less than $1$ it was basically just going to converge and be somewhat less than $\log 2$. But after some thought, I think because the $\sin$ term is basically going to be randomly big or small, irrespective of whether a term is positive or negative, it might diverge (not necessarily to infinity, but it just doesn't have a value to converge to).
I'm fairly familiar with epsilon-deltas for convergence, but I'm not sure where I can find a contradiction stemming from the proof that it converges and I don't know any other relevant ways to prove divergence.
Edit: I feel like I can bound it between 0 and some number, but I can't even prove that. If I can, idk where that goes because bounds are only sufficient for monotone. Maybe I can show an upper bound is impossible and the lack of bound can be an avenue for divergence proof?
