AMC10/12
2019


Problem - 4383

A sequence of numbers is defined recursively by $a_1=1$, $a_2=\frac{3}{7}$, and $$a_n=\frac{a_{n-2}\cdot a_{n-1}}{2a_{n-2}-a_{n-1}}$$

for all $n\ge 3$. Find the value of $a_{2019}$.


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