Question:
The value of $4+\frac{1}{5+\frac{1}{4+\frac{1}{5 \cdot \frac{1}{4+\ldots \infty}}}}$
Correct Option: 1
Solution:
$y=4+\frac{1}{\left(5+\frac{1}{y}\right)}$
$y-4=\frac{y}{(5 y+1)}$
$5 y^{2}-20 y-4=0$
$y=\frac{20+\sqrt{480}}{10}$
$y=\frac{20-\sqrt{480}}{10} \rightarrow$ rejected
$\mathrm{y}=2+\sqrt{\frac{480}{100}}$
Correct with Option (A)