# 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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