JAMB 1985 · UME · Q6

Simplify $\dfrac12 + \cfrac{1}{2 + \cfrac{1}{2 - \cfrac{1}{4 + \frac15}}}$ .

Worked solution (try it first)

Start at the bottom: $4 + \frac15 = \frac{21}{5}$ , so $\dfrac{1}{4 + \frac15} = \frac{5}{21}$ .
Next layer: $2 - \frac{5}{21} = \frac{37}{21}$ , so one over it is $\frac{21}{37}$ .
Next layer: $2 + \frac{21}{37} = \frac{95}{37}$ , so one over it is $\frac{37}{95}$ .
Finally, $\frac12 + \frac{37}{95} = \frac{95 + 74}{190}$
$= \frac{169}{190}$ , option C.