Part 8 (10 points, non-coding task)
Compute
\lim_{n \rightarrow \infty} \ \frac{F_n}{F_{n-1}} .
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Reasoning is required.
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Your answer shall be written in terms of one or two eigenvalues.
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We notice that | \lambda_0 | > 1 and | \lambda_1 | < 1.
Hence,
\begin{align*}
\lim_{n \rightarrow \infty} \ \frac{F_n}{F_{n-1}}
& = \boxed{\lambda_0 } .
\end{align*}
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