let-give-u-n-k-1-n-sin-k-n-k-and-R-find-lim-n-u-n-

Tinku Tara June 4, 2023 Limits 0 Comments

Question Number 28612 by abdo imad last updated on 27/Jan/18

let give u_(n ) = Σ_(k=1) ^n ((sin(kα))/(n+k)) and α∈R find lim _(n→+∞) u_n .

$${let}\:{give}\:\:{u}_{{n}\:} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{sin}\left({k}\alpha\right)}{{n}+{k}}\:{and}\:\:\alpha\in{R} \\ $$$${find}\:{lim}\:_{{n}\rightarrow+\infty} {u}_{{n}} \:\:. \\ $$

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let-give-u-n-k-1-n-sin-k-n-k-and-R-find-lim-n-u-n-

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