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Recurrence Relationshard
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For the recurrence an=3an−1+2an−2a_n = 3a_{n-1} + 2a_{n-2}an​=3an−1​+2an−2​ with characteristic roots r1≈3.56r_1 \approx 3.56r1​≈3.56 and r2≈−0.56r_2 \approx -0.56r2​≈−0.56, what is lim⁡n→∞anan−1\lim_{n \to \infty} \frac{a_n}{a_{n-1}}limn→∞​an−1​an​​ when the sequence is not initially zero?