2. 28 The expression can be simplified in stages as follows:
$$
1+\frac{1}{1+\frac{1}{1+\frac{1}{5}}}=1+\frac{1}{1+\frac{1}{\left(\frac{6}{5}\right)}}=1+\frac{1}{1+\frac{5}{6}}=1+\frac{1}{\left(\frac{11}{6}\right)}=1+\frac{6}{11}=\frac{17}{11}=\frac{a}{b} \text {. }
$$

Hence the value of $a+b$ is $17+11=28$.
2. The value of the expression $1+\frac{1}{1+\frac{1}{1+\frac{1}{1}}}$ is $\frac{a}{b}$, where $a$ and $b$ are integers whose only common factor is 1 . What is the value of $a+b$ ?