Question 86
Let $a_{1}, a_{2}, \ldots$ be an infinite sequence of positive real numbers which satisfies
$$
a_{n+1} \geq a_{n}^{2}+\frac{1}{5}
$$
for every positive integer $n$. Prove that $\sqrt{a_{n+5}} \geq a_{n-5}^{2}$ for each positive integer $n \geq 6$.
$$
a_{n+1} \geq a_{n}^{2}+\frac{1}{5}
$$
for every positive integer $n$. Prove that $\sqrt{a_{n+5}} \geq a_{n-5}^{2}$ for each positive integer $n \geq 6$.