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Question Number 43537 by abdo.msup.com last updated on 11/Sep/18
$${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{{e}^{\frac{{k}}{{n}}} }{{n}} \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} {S}_{{n}} \\ $$
Commented by maxmathsup by imad last updated on 29/Sep/18
$${lim}_{{n}\rightarrow+\infty} \:{S}_{{n}} =\:{lim}_{{n}\rightarrow+\infty} \:\frac{\mathrm{1}}{{n}}\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:{e}^{\frac{{k}}{{n}}} \:\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{{x}} {dx}=\:{e}−\mathrm{1}\:. \\ $$