Sorry for not familiar to Latex or anything like that. I wonder about the convergence of $$ \sum_{n=1}^\infty\frac{1}{n^{2-\sin(n)}}. $$ At first I tried to use comparison test with proper p-series, but I failed to find proper p since $\sup \{\sin(n)\mid n \in \mathbb{N}\}$ is $1$, as far as I know. Is there anyone can determine the convergence of the series?
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Thanks for the answer. But what's the integral of 1/x^(2-sin(x))? How do you know that improper intergral (1/x^(2-sin(x))) diverges? – mymemeisJo May 09 '23 at 13:05
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Oh thanks. I now realized that Answer to the qustion is totally different from thinking the qustion. The prove is so hard.. I really feel thanksful to you. – mymemeisJo May 09 '23 at 13:16