2 Let $x_{i} \geqslant 0(1 \leqslant i \leqslant n, n \geqslant 4), \sum_{i=1}^{n} x_{i}=1$, find the maximum value of $F=\sum_{i=1}^{n} x_{i} x_{i+1}$.
2. By the method similar to the above, the maximum value of $F$ can be obtained as $F\left(\frac{1}{2}, \frac{1}{2}, 0,0, \cdots, 0\right)=\frac{1}{4}$.