Solution
$$3+\frac{1}{1+\frac{1}{2+\frac{1}{4}}}$$
$$3+\frac{1}{1+\frac{1}{\frac{9}{4}}}$$
$$3+\frac{1}{1+\frac{4}{9}}$$
$$3+\frac{1}{\frac{13}{9}}$$
$$3+{\frac{9}{13}}$$
$$\frac{48}{13}$$
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