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 \(a_n = 1 + (a_{nāˆ’1} āˆ’ 1)^2\).

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

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