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# Open problem in mathematics

$\large \int_0^1 \int_0^1 \cdots \int_0^1 \left\{ 1\div \sum_{n=1}^k x_n \right\} ^m \, dx_1 \; dx_2 \cdots dx_k$ Calculate in closed form, the integral above for $$k\geq 3$$ and $$m\geq2$$.

Notation: $$\{ \cdot \}$$ denotes the fractional part function.

Clarification: There are $$k$$ integrals.

This is a part of the set Formidable Series and Integrals

Note by Hummus A
9 months, 3 weeks ago