Question

Lety =$\frac{1}{2+\frac{1}{3+\frac{1}{2+\frac{1}{3+.......}}}}$ What is the value of y?

• A. -2
• B. 2
• C. (-sqrt15-3)/2
• D. (sqrt15-3)/2

Answer 1

The correct option is D (sqrt15-3)/2

Ans: (d)

Given:y=

y =$\frac{1}{2+\frac{1}{3+\frac{1}{2+\frac{1}{3+.......}}}}$

Thus y = $\frac{1}{2+\frac{1}{3+y}}$

$y=\frac{(3+y)}{(6+2y+1)}\Rightarrow 2y^2+7y=3+y;$ On solving, $y=\frac{(-3\pm \sqrt{15})}{2};$ since the given fraction is positive, the value of y is

$\frac{(\sqrt{15}-3)}{2}$(CAT 2004)