Question 60
Two sequences of positive integers, $x_{1}, x_{2}, x_{3}, \ldots$ and $y_{1}, y_{2}, y_{3}, \ldots$, are given, such that
$$
y_{n+1} / x_{n+1} \gt y_{n} / x_{n}
$$
for each $n \geq 1$. Prove that there are infinitely many values of $n$ such that $y_{n} \gt \sqrt{n}$.
$$
y_{n+1} / x_{n+1} \gt y_{n} / x_{n}
$$
for each $n \geq 1$. Prove that there are infinitely many values of $n$ such that $y_{n} \gt \sqrt{n}$.