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Question Number 65677 by mathmax by abdo last updated on 01/Aug/19
$${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{\sqrt{{k}^{\mathrm{2}} +{k}}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{equivalent}\:{of}\:{S}_{{n}} \:{when}\:{n}\rightarrow+\infty \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:\left({S}_{{n}} \right)\:{is}\:{convergent}. \\ $$