Prove that when $p>0,$ the series $$\sum_{n=1}^\infty \sin(n^p)$$ is divergent
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6$\begingroup$ see math.stackexchange.com/q/1558231/87355 $\endgroup$Carlo Beenakker– Carlo Beenakker2024-02-23 12:18:53 +00:00Commented Feb 23, 2024 at 12:18
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1$\begingroup$ What is $n$? And how does $i$ affect the expression? $\endgroup$JRN– JRN2024-02-23 12:44:15 +00:00Commented Feb 23, 2024 at 12:44
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$\begingroup$ $i\mapsto n$, most certainly a typo, I corrected it. $\endgroup$Carlo Beenakker– Carlo Beenakker2024-02-23 13:17:43 +00:00Commented Feb 23, 2024 at 13:17
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1$\begingroup$ The question has just been answered at MSE; see the link Carlo gave above. It's not doing too well here (2 downvotes, 1 close vote currently), but it looks reasonable to me. $\endgroup$Christian Remling– Christian Remling2024-02-23 15:08:56 +00:00Commented Feb 23, 2024 at 15:08
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1$\begingroup$ @Jon: Not until a few minutes ago, but did you see the latest answer, by Sean Eberhard? This settles it, in my opinion. $\endgroup$Christian Remling– Christian Remling2024-02-23 15:22:13 +00:00Commented Feb 23, 2024 at 15:22
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