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Question Number 74353 by mathmax by abdo last updated on 22/Nov/19
$${let}\:\:{A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{{k}+\sqrt{{k}^{\mathrm{2}} +\mathrm{1}}} \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{a}\:{equivalent}\:{of}\:{A}_{{n}} \:\:{when}\:{n}\rightarrow+\infty \\ $$$$ \\ $$