Question Number 30490 by abdo imad last updated on 22/Feb/18
$${f}\:{function}\:{derivable}\:{at}\:{o}\:{and}\:{f}\left(\mathrm{0}\right)=\mathrm{0}\:{let} \\ $$$${S}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} {f}\left(\frac{{k}}{{n}^{\mathrm{2}} }\right)\:\:.{find}\:{lim}_{{n}\rightarrow\infty} {S}_{{n}} . \\ $$