I know $\int_0^{+\infty}\sin(x^2)\ \mathrm dx$ converges, but $\sum\limits_{i=1}^{\infty}\sin(i^2)$ diverges. How to prove it?
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I would guess you mean $\sum_{i=1}^\infty \sin(i^2)$. – Feb 26 '21 at 12:09
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Sorry.I mean $\sum\limits_{i=1}^{\infty}sin(i^2)$ – xcxxcx Feb 26 '21 at 12:10