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Given $$A = 5 + \cfrac{1}{4+\cfrac{1}{3+\cfrac{1}{2+\cfrac{1}{1+\frac{1}{5}}}}}$$. When simplified, A takes the form $$\frac{p}{q}$$ where p, q are positive integers with no common factors. Prove that $$5\frac{1}{5} < A < 5\frac{2}{5}$$.
Correct Answer: 5.2326530612
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