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Question Number 107292 by mathmax by abdo last updated on 09/Aug/20

$$\mathrm{let}{\mathrm{U}}_{\mathrm{n}}=\sum _{\mathrm{k}=1}^{\mathrm{n}}\sin \left(\frac{\mathrm{k}}{\mathrm{n}}\right)\sin \left(\frac{\mathrm{k}}{{\mathrm{n}}^2}\right)$$$$\mathrm{calculate}{\lim }_{\mathrm{n}\to +\mathrm{\infty }}{\mathrm{U}}_{\mathrm{n}}$$

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