let-S-n-x-k-0-n-e-k-sin-k-2-x-1-determine-2-sequence-U-n-x-and-V-n-x-wich-verify-U-n-S-n-V-n-2-let-S-lim-n-S-x-study-the-convergence-of-S-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 63651 by mathmax by abdo last updated on 06/Jul/19

let S_n (x)=Σ_(k=0) ^n e^(−k) sin(k^2 x) 1) determine 2 sequence U_n (x) and V_n (x) wich verify U_n ≤ S_n ≤ V_n 2) let S =lim_(n→+∞) S(x) study the convergence of S.

$${let}\:{S}_{{n}} \left({x}\right)=\sum_{{k}=\mathrm{0}} ^{{n}} \:{e}^{−{k}} {sin}\left({k}^{\mathrm{2}} {x}\right) \\ $$$$\left.\mathrm{1}\right)\:{determine}\:\mathrm{2}\:{sequence}\:\:{U}_{{n}} \left({x}\right)\:{and}\:{V}_{{n}} \left({x}\right)\:{wich}\:{verify}\:{U}_{{n}} \leqslant\:{S}_{{n}} \leqslant\:{V}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{let}\:\:{S}\:={lim}_{{n}\rightarrow+\infty} \:{S}\left({x}\right)\:\:{study}\:{the}\:{convergence}\:{of}\:{S}. \\ $$

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let-S-n-x-k-0-n-e-k-sin-k-2-x-1-determine-2-sequence-U-n-x-and-V-n-x-wich-verify-U-n-S-n-V-n-2-let-S-lim-n-S-x-study-the-convergence-of-S-

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