$\alpha <1$, series $n^{-\alpha} \sum _{k=1}^n \sin (k^2)$ is bounded

Asked Jun 06 '13 at 20:10

Active Jun 06 '13 at 20:10

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Could you help me answer the question, if there exists $\alpha <1$ such that series $n^{-\alpha} \sum _{k=1}^n \sin (k^2)$ is bounded?

asked Jun 06 '13 at 20:10

Hagrid

Maybe it may help to know that the integral sinx² is convergent? (integral test) That might help for your question? – imranfat Jun 06 '13 at 20:46
Integral test does not help at all, since the terms are not positive. – Sungjin Kim Jun 06 '13 at 21:34
1

Try Dirichlet's test. – Mhenni Benghorbal Jun 06 '13 at 21:42
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@MhenniBenghorbal: Can you put it as an answer? I want to see how Dirichlet's test would apply to this problem. – Sungjin Kim Jun 06 '13 at 21:53
http://math.stackexchange.com/questions/2270/convergence-of-sum-limits-n-1-infty-sinnk-n Related – Sungjin Kim Jun 06 '13 at 22:25

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