show that $x_1^2+x_2^2+\cdots+x_{2020}^2\geqslant x_1x_2+x_2x_3+\cdots+x_{2020}x_1$ how can i use AM-GM inequality to show that $$x_1^2+x_2^2+\cdots+x_{2020}^2\geqslant x_1x_2+x_2x_3+\cdots+x_{2020}x_1 ?$$
Where $x_1,x_2,\ldots,x_n$ 
are any real numbers.
to get an idea I tried to do for particular cases with $n=3,4.$
for $n=3$, I could use AM-GM doing $$x_1^2+x_2^2+x_3^2=\frac{x_1^2+x_2^2}{2}+\frac{x_2^2+x_3^2}{2}+\frac{x_3^2+x_1^2}{2}\geqslant x_1x_2+x_2x_3+x_3x_1.$$
for $n=4$  couldn't with that same idea. 
but it is possible to show 
developing the inequality below $$(x_1-x_2)^2+(x_2-x_3)^2+(x_3-x_4)^2+(x_4-x_1)^2 \geqslant 0.$$

The idea is the same:
$$
x_1x_2 + x_2x_3 + \cdots + x_{2020}x_1 \leq \frac{x_1^2 + x_2^2}{2} + \frac{x_2^2 + x_3^2}{2} + \cdots + \frac{x_{2020}^2 + x_1^2}{2} = x_1^2 + x_2^2 + \cdots + x_{2020}^2
$$
