Question: Let a n = max {sin 1, sin 2, . . . , sin n}, for n = 1, 2, 3, . . ., where

Let a_n = max {sin 1, sin 2, . . . , sin n}, for n = 1, 2, 3, . . ., where max { . . .} denotes the maximum element of the set. Does {a_n} converge? If so, make a conjecture about the limit.

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