# Fraction

Calculus Level 3

$\large 1 + \cfrac{1}{2 + \cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{1 + \ddots}}}}$

If the infinitely nested fraction above is equal to $$\dfrac{a+\sqrt b}c$$, where $$a,b$$ and $$c$$ are positive integers with $$b$$ square-free, find $$a+b+c$$.

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