Question

Evaluate the continued fraction: $x = 2 + \frac{1}{3+\frac{1}{4+\frac{1}{2}}}$

• A. 67/29
• B. 41/17
• C. 45/19
• D. 47/20

Answer 1

Answer:

A. 67/29

Evaluate from the innermost fraction outward:

$x = 2 + \frac{1}{3+\frac{1}{4+\frac{1}{2}}}$

First,

$4+\frac{1}{2}=\frac{9}{2}$

So,

$\frac{1}{4+\frac{1}{2}}=\frac{1}{9/2}=\frac{2}{9}$

Now,

$3+\frac{2}{9}=\frac{29}{9}$

Thus,

$\frac{1}{3+\frac{2}{9}}=\frac{9}{29}$

Finally,

$x=2+\frac{9}{29}$

$2+\frac{9}{29}=\frac{67}{29}$

Therefore,

$x=\frac{67}{29}$