# Divergence or convergence of a series

Does this converge or diverge? $$\sum_{n=1}^\infty\frac{1+\sin^2n}{n}$$ I tried the divergence test and got infinity. But the graph of the functions shows it converges to zero. Any suggestions? We are not allowed to use delta - epsilon proofs. It is a Calculus II question.

We have that $$\sum_{n=1}^\infty\frac{1+\sin^2n}n\ge\sum_{n=1}^\infty\frac1n$$ since $\sin^2n\ge0$ and the latter series diverges. Hence, the former series diverges too.