I see that quite a few questions on infinite series have been asked recently and figured why not continue the trend!
going through my lectures and textbooks, I understand $\sin^2n$ is bounded by 0 and 1, I understand that something like $\cos\pi n$ is just an alternating series in disguise, however, I cannot come up with a solid strategy for when it is just $\sin(n)$
So for example, my problem I am currently stuck on: $\sum_{i=1}^\infty {\sin(n)\over (5+2n^2)} $
Now I know how you would tackle something like $\sum_{i=1}^\infty \sin({1\over n}) $ but the n term isn't attached to the sin function. In my problem above I believe that is what is screwing with me.
My intuition tells me to do a comparison test to $\sum_{i=1}^\infty \sin({1\over n^2}) $
If someone could kindly explain it would be much appreciated!