Number Theory

$4 + \frac{1}{4 + \frac{1}{4 + \frac{1}{4}}}$

$4+\frac{1}{4+\frac{1}{\frac{5}{4}}}$

$4 + \frac{1}{4+\frac{4}{5}}$

$4+\frac{1}{\frac{24}{5}}$

$4+\frac{5}{24}$

$\mathbf{\frac{101}{24}}$