# Calculus - Inadequate Information #1

Calculus Level 3

Two infinite sequences $$\{a_n\}$$ and $$\{b_n\}$$ satisfy the following recurrence relations: $\cases{a_{n+1}=a_n+2b_n \\\\ b_{n+1}=a_n+b_n.}$ Given that $$a_nb_n>0$$ for any positive integer $$n,$$ $\lim_{n\to\infty}{\dfrac{b_n}{a_n}}=\dfrac{N\sqrt{Q}}{D},$ where positive integers $$D$$ and $$N$$ are coprime and $$Q$$ is a square-free integer.

Find the value of $$N+Q+D.$$

This problem is a part of <Calculus - Inadequate Information> series.

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