Simple recurrence relation - 1D

Question

I know this is a very simple recurrence relation, but how would you go on solving it?

$$x(n+1)=\frac{x(n)}{1+x(n)}$$

Answer 1

Hint: Let $y(n)=\frac{1}{x(n)}$. The recurrence for $y(n)$ is very pleasantly simple.