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Ayaan Barr 2022-07-04 Answered
How to prove lim sup n | sin ( n ) | = 1?
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Answers (1)

poquetahr
Answered 2022-07-05 Author has 18 answers
See this article, a special case is that there is two increasing sequences of odd positive integers ( p n ) , ( q n ) such that
| π 2 p n q n | 1 q n 2 , n > 1.
Note that sin | x | = | sin x | for x [ 0 , π ], then
sin | q n π 2 p n | = | cos p n | < 1 q n 0.
therefore | sin p n | 1
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