let-U-n-k-1-n-sin-k-n-sin-k-n-2-calculate-lim-n-U-n-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

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

let U_n =Σ_(k=1) ^n sin((k/n))sin((k/n^2 )) calculate lim_(n→+∞) U_n

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

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