Let $f(x_1,\ldots , x_n) = \frac{x_1}{x_2+x_3} + \frac{x_2}{x_3+x_4} + \cdots + \frac{x_n}{x_1+x_2}$, defined for $x_i>0$.

- Is there $(x_1, \ldots ,x_n)\in {\mathbb{R}^*_+}^n$ such that $f(x_1,\ldots , x_n) < n/2$?
- Can we find $\inf_{x_i>0}f(x_1,\ldots , x_n)$?