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let-S-n-k-1-n-1-k-2-k-1-find-a-equivalent-of-S-n-when-n-2-prove-that-S-n-is-convergent-

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

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