I'm trying to figure out whether the following series converges absolutely or conditionally or whether it diverges. I am stuck on the following one that involved both sin and cosine: $$ \sum_{n=1}^{\infty} \frac{\sin(n)}{n^2+\cos(n)} $$ Any guidance would be greatly appreciated however :)
2026-03-27 07:48:27.1774597707
Convergence of a sequence with both sin and cos
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HINT:
$$\left|\frac{\sin n}{n^2+\cos n}\right|\le \frac{1}{n^2-1}$$
for $n>1$.