Sean $a_{1},a_{2},\cdots,a_{n}$ números reales positivos que satisfacen $a_{1} + a_{2} + \cdots + a_{n} = 1$. Pruebe que \[\left(a_{1}a_{2} + a_{2}a_{3} + \cdots + a_{n}a_{1}\right)\left(\frac {a_{1}}{a_{2}^2 + a_{2}} + \frac {a_{2}}{a_{3}^2 + a_{3}} + \cdots + \frac {a_{n}}{a_{1}^2 + a_{1}}\right)\ge\frac {n}{n + 1}\]