Question 35
All numbers of the form $2^{k}3^{s}$ ($k, s$ are non-negative whole numbers) were written in increasing order $1, 2, 3, 4, 6, 8, 9, 12, \ldots$ and formed the sequence $a_n$. Prove that there are infinitely many numbers $n$ satisfying the condition
$$
\frac{a_{n+1}}{a_n} \lt 1 + \frac{1}{10^{2014}}
$$
$$
\frac{a_{n+1}}{a_n} \lt 1 + \frac{1}{10^{2014}}
$$