Question

If $x=1+\frac{1}{3+\frac{1}{2+\frac{1}{3+\frac{1}{2.00}}}}.$ Then value of $x$ is

• A. $\frac{881}{55}$
• B. $\sqrt{\frac{3}{2}}$
• C. $\sqrt{\frac{7}{3}}$
• D. $\sqrt{\frac{5}{3}}$

Answer 1

The correct option is A $\frac{881}{55}$

Consider the given equation,

$x=1+\frac{1}{3+\frac{1}{2+\frac{1}{3+\frac{1}{2.00}}}}$

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

$x=1+\frac{1}{3+\frac{1}{2+\frac{1}{\frac{7}{2}}}}$

$x=1+\frac{1}{3+\frac{1}{2+\frac{2}{7}}}$

$x=1+\frac{1}{3+\frac{1}{\frac{16}{7}}}$

$x=1+\frac{1}{3+\frac{7}{16}}$

$x=1+\frac{1}{\frac{55}{16}}$

$x=1+\frac{16}{55}$

$x=1+\frac{16}{55}$

$x=\frac{881}{55}$

Hence, this is the answer.