Recurring Theme

Calculus Level 5

Consider a recurrence relation, \(a_{n+3}=2a_{n+2}+a_{n+1}-a_n\) for \(n\geq 0\) and \(a_0=1\), find the sum of all possible values of \(\displaystyle \lim_{n\to\infty}\frac{a_{n+1}}{a_n}\), rounded to three significant figures. Here, \(a_1\) and \(a_2\) are arbitrary real numbers.

If you reach the conclusion that the limit fails to exist in some cases, enter 0.666

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