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Question Number 34693 by math khazana by abdo last updated on 09/May/18

let S_n = (1/(n(√n))) Σ_(k=1) ^n  [(√k) ]  find lim_(n→+∞)  S_n

$${let}\:{S}_{{n}} =\:\frac{\mathrm{1}}{{n}\sqrt{{n}}}\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\left[\sqrt{{k}}\:\right] \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} \:{S}_{{n}} \\ $$

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