11
votes
0answers
290 views

Two questions about weakly convergent series related to $\sin(n^2)$ and Weyl's inequality

By using partial summation and Weyl's inequality, it is not hard to show that the series $\sum_{n\geq 1}\frac{\sin(n^2)}{n}$ is convergent. Is is true that ...
1
vote
1answer
201 views

Probability that two numbers do not follow each other and are distributed over a sequence

Assume a sequence $S$ of numbers out of the set $N={1..n}$. Example: $$S = "123312"$$ Set of all pairs would be: $$M = (2,3),(3,3), (3,1)$$ Not in $M$: $(1,1)$ : not occuring in the sequence next ...