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.
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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.