Which of the following represents the correct simplified value of the continued fraction:

$$
z = 3 + \frac{1}{4 + \frac{1}{4 + \frac{1}{4}}}
$$

Question

Which of the following represents the correct simplified value of the continued fraction:

$$
z = 3 + \frac{1}{4 + \frac{1}{4 + \frac{1}{4}}}
$$

Accepted Answer

Work from the bottom up.

1. Bottom term: $4$.
2. Next: $4 + \frac{1}{4} = \frac{17}{4}$.
3. Next: $4 + \frac{1}{17/4} = 4 + \frac{4}{17} = \frac{72}{17}$.
4. Finally: $z = 3 + \frac{1}{72/17} = 3 + \frac{17}{72} = \frac{233}{72}$.

**So the value is $\frac{233}{72}$.**
FINAL_ANSWER: a

Answer

Answer

Answer