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Omni-MATH / Let the sequence {a_(i)}_(i=0)^(∞) be defined by a₀=(1)/(2) and a_(n)=1+(a_(n−1)−1)². Find the product ∏_(i=0)^(∞)a_(i)=a₀a₁a₂

Problem

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problem

Let the sequence {ai}i=0∞\left\{a_{i}\right\}_{i=0}^{\infty} be defined by a0=12a_{0}=\frac{1}{2} and an=1+(an−1−1)2a_{n}=1+\left(a_{n-1}-1\right)^{2}. Find the product ∏i=0∞ai=a0a1a2\prod_{i=0}^{\infty} a_{i}=a_{0} a_{1} a_{2}
Plain-text mathematical notation (without MathML)
Let the sequence {a_(i)}_(i=0)^(∞) be defined by a₀=(1)/(2) and a_(n)=1+(a_(n−1)−1)². Find the product ∏_(i=0)^(∞)a_(i)=a₀a₁a₂
Original LaTeX notation
Let the sequence $\left\{a_{i}\right\}_{i=0}^{\infty}$ be defined by $a_{0}=\frac{1}{2}$ and $a_{n}=1+\left(a_{n-1}-1\right)^{2}$. Find the product $$\prod_{i=0}^{\infty} a_{i}=a_{0} a_{1} a_{2}$$

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Source and history

task_id
e60cb3ff-6611-583f-acb4-3b1013be8e12
task_key
test--e60cb3ff-6611-583f-acb4-3b1013be8e12
task_revision_id
1
config / split
/ test

Official source

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