# Weird Recursion-2

Calculus Level 5

A recurrence relation is given by $$b_{ 0 }=\dfrac { 7 }{ 2 }$$ and $$b_{ n }=8-\dfrac { 7 }{ b_{ n-1 } }$$.

If $$b_{ n }=\dfrac { A+B\cdot{ C }^{ n } }{ A+B\cdot{ C }^{ n-1 } }$$ and $$\displaystyle \lim _{ n\to \infty }{ b_{ n } } = F$$, where $$A,B$$ and $$C$$ are positive integers and $$\gcd(A,B)=1$$ then find $$A + B + C + F$$.

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