My Calculus II teacher left us the task of finding a sequence that is conditionally convergent, and that if we multiply it by $(-1)^n$ it converges. I think that sequence could be $\frac{sen(n)}{n}$. But first I have to prove that it is conditionally convergent, for that I will use the Dirichlet test. And one of his hypotheses is that the partial sums of $\Sigma_{n=1}^\infty \sin(n)$ are bounded , but I don't know how to do it. I would appreciate if you do not use very complicated things in the proof, since I would also have to demonstrate them.
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Have you looked for similar questions here? Or similar techniques? – rtybase Jun 14 '20 at 10:19
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Looks like you have a minor typo... do you mean sequence $\frac{sin (n)}{n}$? – coffeemath Jun 14 '20 at 10:24