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the series : $$\sum_{n \geq 1} \frac{1}{n^{\alpha+\sin(n)}}$$

according to answers to a question I previously asked here on MSE

there's no way I can compare to a p-series.

it's been some time that I encountered this series and I still have no idea how to tackle it.

any help would be greatly appreciated

the_firehawk
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  • I do not understand what you do not like about the answer given to the prior question. It proves that for $\alpha >1$ the limit is 0, for $\alpha < -1$ the limit is $\infty$ and for the other cases, the limit does not exist. – Fabian Jun 02 '18 at 14:35
  • @Fabian I didn't say I didn't like the answer given there. Im just saying thanks to the answers now I know trying to make a comparison test with a p-series is impossible – the_firehawk Jun 02 '18 at 14:37

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