Find a closed form of
\[ \int_{0}^{1} \ldots \int_{0}^{1} \left \{ \dfrac{x_{1}}{x_{2}} \right \} \left \{\dfrac{x_{2}}{x_{3}}\right \} \ldots \left \{\dfrac{x_{n-1}}{x_{n}}\right \} \left \{\dfrac{x_{n}}{x_{1}}\right \} \ \mathrm{d}x_{1} \ \mathrm{d}x_{2} \ldots \mathrm{d}x_{n} \quad ; \quad n \geq 3 \]
Notation : denotes fractional part function.
This is a part of the set Formidable Series and Integrals
Easy Math Editor
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2^{34}
a_{i-1}
\frac{2}{3}
\sqrt{2}
\sum_{i=1}^3
\sin \theta
\boxed{123}
Comments
Damn. Its looks so difficult :D it is easier to solve a rubic's cube in 1 min rather solving this problem :p
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Case n=2 is very simple.
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ya right :)
i was making good progress,but i got stuck at
∫01⌊x2x1⌋⌊x1x3⌋dx1
:(
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okay i will try