Find the value of:

The correct answer is Option (4) → \(\frac{6}{11}\)

A continued fraction is simplified from the bottom up, one level at a time.

• Innermost level: \(\displaystyle 1+\frac{1}{5}=\frac{6}{5}\)

• Next level: \(\displaystyle \frac{1}{6/5}=\frac{5}{6}\), so \(\displaystyle 1+\frac{5}{6}=\frac{11}{6}\)

• Outer level: \(\displaystyle \frac{1}{11/6}=\frac{6}{11}\)