study-the-convergence-of-u-n-k-0-n-1-1-k-2-argsh-n-and-v-n-k-0-n-1-1-k-2-

Question Number 28538 by abdo imad last updated on 26/Jan/18

$${study}\:{the}\:{convergence}\:{of} \\ $$$${u}_{{n}\:} \:\:=\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{k}^{\mathrm{2}} }}\:\:−{argsh}\left({n}\right)\:\:{and} \\ $$$${v}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{k}^{\mathrm{2}} }}\:\:. \\ $$$$ \\ $$

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