Find all positive integers
![a_1, a_2, \ldots, a_n](/media/m/9/2/c/92c14c25a50ea2e6e7d3f457e8ea9a16.png)
such that
where
![a_0 = 1](/media/m/0/5/5/05531a4642948e069319f5338873b883.png)
and
![(a_{k+1}-1)a_{k-1} \geq a_k^2(a_k - 1)](/media/m/c/2/3/c23526b025c3af4c86211f0ec5aabdf2.png)
for
![k = 1,2,\ldots,n-1](/media/m/6/2/8/6281d130925b4c4bbeeb11a6946bb555.png)
.
%V0
Find all positive integers $a_1, a_2, \ldots, a_n$ such that
$$\frac{99}{100} = \frac{a_0}{a_1} + \frac{a_1}{a_2} + \cdots + \frac{a_{n-1}}{a_n},$$
where $a_0 = 1$ and $(a_{k+1}-1)a_{k-1} \geq a_k^2(a_k - 1)$ for $k = 1,2,\ldots,n-1$.