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occurred Nov 16, 2020 at 13:26

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edit approved Nov 16, 2020 at 9:03

gmvh

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ca.classical-analysis-and-odes sequences-and-series

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edited Nov 16, 2020 at 8:02

YCor

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How to show this series converges $\sum\limits_{n=1}^\infty n^{-1/2}\sin(n)\sin(n^2$n^2)$

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edited Nov 16, 2020 at 7:51

Martin Sleziak

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How to show this series converges $\sum\limits_{n=1}^\infty n^{-1/2}\sin(n)\sin(n^2$

I want to see if this series converges or not: $$ \sum_{n=1}^\infty n^{-1/2}\sin(n)\sin(n^2). $$
I tried comparisioncomparison tests but nothing. I saw that integral criteria works but I don't know how to show that.

Thank you

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edited Nov 16, 2020 at 1:02

David Roberts ♦

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edited Nov 16, 2020 at 0:49

ursuv2

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edited Nov 16, 2020 at 0:41

Konstantinos Kanakoglou

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asked Nov 16, 2020 at 0:29

ursuv2

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How to show this series converges $\sum\limits_{n=1}^\infty n^{-1/2}\sin(n)\sin(n^2$n^2)$

How to show this series converges $\sum\limits_{n=1}^\infty n^{-1/2}\sin(n)\sin(n^2$

How to show this series converges

How to show this series converges $\sum\limits_{n=1}^\infty n^{-1/2}\sin(n)\sin(n^2$