# Add a reciprocal, repeat

Algebra Level 5

Let $$a_n$$ be a sequence of positive real numbers defined by $$a_ 1 = 1$$ and

$a_{n+1} = a_n + \frac{1}{a_n} \text{ for } n\geq 1.$

Evaluate $$\lfloor a_{100000} \rfloor$$.

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