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Question Number 32008 by gunawan last updated on 18/Mar/18

$$\underset{n\to \mathrm{\infty }}{\lim }[{\left(\frac{1}{n}\right)}^n+{\left(\frac{2}{n}\right)}^n+..+{\left(\frac{n}{n}\right)}^n]=...$$

Commented by JDamian last updated on 18/Mar/18

$$Iguesstheuseof\mathit{x}isatypo.$$

Commented by gunawan last updated on 18/Mar/18

$$\mathrm{oh}{\mathrm{i}}^{\prime }\mathrm{m}\mathrm{sorry}$$

Commented by gunawan last updated on 18/Mar/18

$$\mathrm{her}\mathrm{question}\mathrm{has}\mathrm{been}\mathrm{changed},\mathrm{Sir}$$

Answered by ajfour last updated on 18/Mar/18

$$=\underset{n\to 0}{\lim }n\left[\frac{1}{n}\underset{r=1}{\sum ^n}{\left(\frac{r}{n}\right)}^n\right]$$$$=\underset{n\to 0}{\lim }n{\int }_0^1{x}^{n}dx=\underset{n\to 0}{\lim }\frac{n}{n+1}=1.$$

Commented by gunawan last updated on 18/Mar/18

$$\mathrm{wow}$$$$\mathrm{thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{sir}$$

Commented by gunawan last updated on 18/Mar/18

$$\mathrm{sorry}\mathrm{to}\mathrm{touch}$$

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