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Simplify : $$1 + {2 \over {1 + {3 \over {1 + {4 \over 5}}}}}$$

Simplify : $$1 + {2 \over {1 + {3 \over {1 + {4 \over 5}}}}}$$ Correct Answer $$\frac{7}{4}$$

$$\eqalign{ & 1 + \frac{2}{{1 + \frac{3}{{1 + \frac{4}{5}}}}} \cr & = 1 + \frac{2}{{1 + \frac{3}{{\frac{9}{5}}}}} \cr & = 1 + \frac{2}{{1 + \frac{5}{3}}} \cr & = 1 + \frac{2}{{\frac{8}{3}}} \cr & = 1 + \frac{3}{4} \cr & = \frac{7}{4} \cr} $$

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