Question

The value of $4-\frac{5}{1+\frac{1}{3+\frac{1}{2+\frac{1}{4}}}}$ is

• A. $\frac{40}{31}$
• B. $\frac{4}{9}$
• C. $\frac{1}{8}$
• D. $\frac{31}{40}$

Answer 1

The correct option is C $\frac{1}{8}$

Let the expression be

$E=4-\frac{5}{1+\frac{1}{3+\frac{1}{2+\frac{1}{4}}}}$

$\Rightarrow E=4-\frac{5}{1+\frac{1}{3+\frac{4}{9}}}$

$\Rightarrow E=4-\frac{5}{1+\frac{9}{31}}$

$\Rightarrow E=4-\frac{5\times 31}{40}$

$\Rightarrow E=4-\frac{31}{8}$

$\Rightarrow E=\frac{1}{8}$

Hence, $\frac{1}{8}$ is correct.