# An algebra problem on sequences

Algebra Level 3

Let the sequence $$\left \{ a_i \right \}_{i=0}^\infty$$ be defined by $$a_0 = \frac 12$$ and $$a_n = 1 + (a_{n−1} − 1)^2$$.

Find $$\displaystyle \prod_{i=0}^\infty a_i$$.

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