Problem:
Two sequence $a_n, b_n$ which satisfy
\begin{cases} a_{n+1}=n^2a_n -2b_n \\ b_{n+1}=n^2b_n +2a_n \end{cases} and$$a_1 =1, \quad b_1 = 0$$Find $$\lim_{n\to\infty} \frac{b_n}{a_n}$$
How can I approach? I couldn't find any relation of $a_n$ and $b_n$.
from Hot Weekly Questions - Mathematics Stack Exchange
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