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 \(A+B\)

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