CAT 2004 Question Paper Question 16
Question 16
Let $$ y = \frac{1}{2+\frac{1}{3+\frac{1}{2+\frac{1}{3+…}}}}$$. Then y equals?
Solution
$$ y = \frac{1}{2+\frac{1}{3+\frac{1}{2+\frac{1}{3+…}}}}$$
which is equal to $$ y = \frac{1}{2+\frac{1}{3+y}} $$ solving we get
$$ y = \frac{3+y}{7+2y} $$ we get
$$2y^2+6y-3=0$$ .
Solution of this equation is $$\frac{\sqrt{15}-3}{2}$$.
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