Problem

Source: CWMO 2004, problem 5

Tags: induction, arithmetic sequence, algebra proposed, algebra



The sequence $\{a_n\}_{n}$ satisfies the relations $a_1=a_2=1$ and for all positive integers $n$, \[ a_{n+2} = \frac 1{a_{n+1}} + a_n . \] Find $a_{2004}$.