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Question Number 32344 by abdo imad last updated on 23/Mar/18

let  u_n = Σ_(k=1) ^n  ch((1/(√(k+n)))) −n  prove that u_n  is convergent and find its limit.

$${let}\:\:{u}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{ch}\left(\frac{\mathrm{1}}{\sqrt{{k}+{n}}}\right)\:−{n} \\ $$$${prove}\:{that}\:{u}_{{n}} \:{is}\:{convergent}\:{and}\:{find}\:{its}\:{limit}. \\ $$

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