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Question Number 101770 by john santu last updated on 04/Jul/20

$$\underset{n\to \mathrm{\infty }}{\lim }\frac{1^{13}+2^{13}+3^{13}+4^{13}+...+n^{13}}{n^{14}}?$$

Commented by Dwaipayan Shikari last updated on 04/Jul/20

$$\frac{1}{14}$$

Commented by john santu last updated on 04/Jul/20

$$yes.n\to \mathrm{\infty }.typo.$$

Answered by bemath last updated on 05/Jul/20

$$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\frac{1}{\mathrm{n}}\underset{\mathrm{i}=1}{\sum ^{13}}{\left(\frac{i}{n}\right)}^{13}=\underset{0}{\stackrel{1}{\int }}{x}^{13}dx$$$$=\frac{1}{14}.★$$

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