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find-lim-n-U-n-with-U-n-k-1-n-ch-1-k-n-n-




Question Number 50404 by Abdo msup. last updated on 16/Dec/18
find lim_(n→+∞)  U_n   with  U_n =(Σ_(k=1) ^(n )  ch((1/( (√(k+n))))))−n
$${find}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \:\:{with} \\ $$$${U}_{{n}} =\left(\sum_{{k}=\mathrm{1}} ^{{n}\:} \:{ch}\left(\frac{\mathrm{1}}{\:\sqrt{{k}+{n}}}\right)\right)−{n} \\ $$$$ \\ $$

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