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Question Number 50391 by Abdo msup. last updated on 16/Dec/18
$${let}\:{f}\left({t}\right)\:=\frac{{t}}{\sqrt{\mathrm{1}+{t}}} \\ $$$${study}\:{the}\:{sequence}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:{f}\left(\frac{{k}}{{n}^{\mathrm{2}} }\right). \\ $$