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let-S-n-x-k-1-n-sin-kx-k-2-k-1-find-lim-n-S-n-x-




Question Number 30556 by abdo imad last updated on 23/Feb/18
let  S_n (x)= Σ_(k=1) ^n    ((sin(kx))/(k^2 (k+1)))  find lim_(n→∞) S_n (x).
$${let}\:\:{S}_{{n}} \left({x}\right)=\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\:\frac{{sin}\left({kx}\right)}{{k}^{\mathrm{2}} \left({k}+\mathrm{1}\right)}\:\:{find}\:{lim}_{{n}\rightarrow\infty} {S}_{{n}} \left({x}\right). \\ $$

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