Solution: The recurrence $ a_n+1 = a_n - raca_n^36 $ resembles the Taylor series for $ rctan(u) $, where $ racddu rctan(u) = rac11 + u^2 $. However, the recurrence is not exact. Assume the limit $ L $ exists. Then $ L = L - racL^36 \Rightarrow racL^36 = 0 \Rightarrow L = 0 $. To confirm convergence, note $ a_1 = \pi/2 pprox 1.57 > 1 $, and $ a_n+1 = a_n(1 - raca_n^26) $. Since $ a_1 < \sqrt6 $, $ a_n $ is decreasing and bounded below by 0. By monotone convergence, $ a_n o 0 $. - Crosslake