I want to see if this series converges or not:
$$
\sum_{n=1}^\infty n^{-1/2}\sin(n)\sin(n^2).
$$
I tried comparison tests but nothing. I saw that integral criteria works but I don't know how to show that.
Thank you
How to show this series converges $\sum\limits_{n=1}^\infty n^{-1/2}\sin(n)\sin(n^2$
ursuv2
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