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Question Number 155146 by amin96 last updated on 26/Sep/21

$$\mathcal{L}={\int }_0^1{\int }_0^1{\int }_0^1{\left(\left\{\frac{x}{y}\right\}\left\{\frac{y}{z}\right\}\left\{\frac{z}{x}\right\}\right)}^{n}dxdydz=?$$

Answered by yeti123 last updated on 26/Sep/21

$$\mathcal{L}={\int }_0^1{\int }_0^1{\int }_0^1{\left(\left\{\frac{x}{y}\right\}\left\{\frac{y}{z}\right\}\left\{\frac{z}{x}\right\}\right)}^{n}dxdydz$$$$={\int }_0^1{\int }_0^1{\int }_0^1{\left(\frac{x}{x}\times \frac{y}{y}\times \frac{z}{z}\right)}^{n}dxdydz$$$$={\int }_0^1{\int }_0^1{\int }_0^1{\left(1\right)}^{n}dxdydz$$$$={\int }_0^1{\int }_0^1{\int }_0^{1}dxdydz$$$$=1$$

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