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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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How to show this series converges $\sum\limits_{n=1}^\infty n^{-1/2}\sin(n)\sin(n^2)$ [closed]
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 t …