Question 87
Consider the two infinite sequences $a_{0}, a_{1}, a_{2}, \ldots$ and $b_{0}, b_{1}, b_{2}, \ldots$ of real numbers such that $a_{0}=0, b_{0}=0$ and
$$
a_{k+1}=b_{k}, \quad b_{k+1}=\frac{a_{k} b_{k}+a_{k}+1}{b_{k}+1}
$$
for each integer $k \geq 0$. Prove that $a_{2024}+b_{2024} \geq 88$.
$$
a_{k+1}=b_{k}, \quad b_{k+1}=\frac{a_{k} b_{k}+a_{k}+1}{b_{k}+1}
$$
for each integer $k \geq 0$. Prove that $a_{2024}+b_{2024} \geq 88$.