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Question Number 161407 by mathlove last updated on 17/Dec/21

Answered by puissant last updated on 18/Dec/21

$$\mathrm{\Omega }={\int }_0^1\sqrt{x\sqrt[3]{x\sqrt[4]{x\sqrt[5]{...}}}}dx={\int }_0^1{x}^{\frac{1}{2}+\frac{1}{6}+\frac{1}{24}...}dx$$$$={\int }_0^1{x}^{\underset{n=2}{\sum ^{\mathrm{\infty }}}\frac{1}{n!}}dx={\int }_0^1{x}^{e-1}dx=\frac{1}{e}{\left[x^e\right]}_0^1=\frac{1}{e}..$$$$..........\mathcal{L}epuissant...........$$

Commented by Tawa11 last updated on 18/Dec/21

$$\mathrm{Great}\mathrm{sir}$$

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