# Recursive sequence

Algebra Level 3

The sequence $$a_n$$ is defined as $$a_0 = 1$$ and $$a_n=\dfrac{a_{n-1}}{1+a_{n-1}}$$ when $$n > 1$$.

If $$a_{2016} = \dfrac{A}{B}$$, where $$A$$ and $$B$$ are two coprime positive integers, find $$A+B$$

×