Question 158
Let the sequence $(a_n)$ be constructed in the following way:
$$
a_1 = 1,\ a_2 = 1,\ a_{n+2} = a_{n+1} + \frac{1}{a_n},\ n = 1, 2, \dots
$$
Prove that $a_{180} \gt 19$.
$$
a_1 = 1,\ a_2 = 1,\ a_{n+2} = a_{n+1} + \frac{1}{a_n},\ n = 1, 2, \dots
$$
Prove that $a_{180} \gt 19$.