$$\displaystyle\sum\limits_{n=1}^\infty \dfrac{n^{-1/2}}{2+\sin^2(n)}$$
I tried the divergence test but it approaches 0.
It's not a geometric series.
Doubt I could apply the integral test.
Not a p-series nor an alternating series.
Can't use root test.
I suppose I am left with either ratio test or a comparison test but I couldn't figure those out.
Advice?