# SAT1000 - P491

Algebra Level 3

Given that $f(x)=\dfrac{1}{1+x}$. $\{a_n\}$ is a sequence whose terms are all positive so that $a_1=1, a_{n+2}=f(a_n)$.

If $a_{2010}=a_{2012}$, find the value of $\lfloor 1000(a_{20}+a_{11}) \rfloor$.

Have a look at my problem set: SAT 1000 problems

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