$$1+ \frac{ 1 }{ 2 } + 2 \frac { 1 } { 3 }$$
$\frac{23}{6}\approx 3.833333333$
$$\frac{2}{2}+\frac{1}{2}+\frac{2\times 3+1}{3}$$
$$\frac{2+1}{2}+\frac{2\times 3+1}{3}$$
$$\frac{3}{2}+\frac{2\times 3+1}{3}$$
$$\frac{3}{2}+\frac{6+1}{3}$$
$$\frac{3}{2}+\frac{7}{3}$$
$$\frac{9}{6}+\frac{14}{6}$$
$$\frac{9+14}{6}$$
$$\frac{23}{6}$$
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$\frac{23}{2 \cdot 3} = 3\frac{5}{6} = 3.8333333333333335$
