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Omni-MATH / Let {a_(i)}_(i≥0) be a sequence of real numbers defined by a_(n+1)=a_(n)²−(1)/(2^(2020⋅2^(n)−1)) for n≥0. Determine the largest value for a₀ such that {a_(i)}_(i≥0) is bounded.

Problem

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problem

Let {ai}i≥0\{a_{i}\}_{i \geq 0} be a sequence of real numbers defined by an+1=an2−122020⋅2n−1a_{n+1}=a_{n}^{2}-\frac{1}{2^{2020 \cdot 2^{n}-1}} for n≥0n \geq 0. Determine the largest value for a0a_{0} such that {ai}i≥0\{a_{i}\}_{i \geq 0} is bounded.
Plain-text mathematical notation (without MathML)
Let {a_(i)}_(i≥0) be a sequence of real numbers defined by a_(n+1)=a_(n)²−(1)/(2^(2020⋅2^(n)−1)) for n≥0. Determine the largest value for a₀ such that {a_(i)}_(i≥0) is bounded.
Original LaTeX notation
Let $\{a_{i}\}_{i \geq 0}$ be a sequence of real numbers defined by $a_{n+1}=a_{n}^{2}-\frac{1}{2^{2020 \cdot 2^{n}-1}}$ for $n \geq 0$. Determine the largest value for $a_{0}$ such that $\{a_{i}\}_{i \geq 0}$ is bounded.

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Source and history

task_id
3a256584-34c3-580f-b7a5-d799616cf627
task_key
test--3a256584-34c3-580f-b7a5-d799616cf627
task_revision_id
1
config / split
/ test

Official source

initial import