Question 65
Let the sequence $\{a_{i}\}_{i=0}^{\infty}$ be defined by $a_{0}=\frac{1}{2}$ and $a_{n}=1+(a_{n-1}-1)^{2}$. Find the product
$$
\prod_{i=0}^{\infty} a_{i} = a_{0} a_{1} a_{2} \ldots
$$
$$
\prod_{i=0}^{\infty} a_{i} = a_{0} a_{1} a_{2} \ldots
$$