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Omni-MATH / Let n be a positive integer. Find the largest nonnegative real number f(n) (depending on n ) with the following property: whenever a₁,a₂,…,a_(n) are real numbers such that …

Problem

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problem

Let nn be a positive integer. Find the largest nonnegative real number f(n)f(n) (depending on nn ) with the following property: whenever a1,a2,…,ana_{1}, a_{2}, \ldots, a_{n} are real numbers such that a1+a2+⋯+ana_{1}+a_{2}+\cdots+a_{n} is an integer, there exists some ii such that \left|a_{i}-\frac{1}{2}\right| \geq f(n)$.
Plain-text mathematical notation (without MathML)
Let n be a positive integer. Find the largest nonnegative real number f(n) (depending on n ) with the following property: whenever a₁,a₂,…,a_(n) are real numbers such that a₁+a₂+⋯+a_(n) is an integer, there exists some i such that \left|a_{i}-\frac{1}{2}\right| \geq f(n)$.
Original LaTeX notation
Let $n$ be a positive integer. Find the largest nonnegative real number $f(n)$ (depending on $n$ ) with the following property: whenever $a_{1}, a_{2}, \ldots, a_{n}$ are real numbers such that $a_{1}+a_{2}+\cdots+a_{n}$ is an integer, there exists some $i$ such that \left|a_{i}-\frac{1}{2}\right| \geq f(n)$.

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Source and history

task_id
2d572c41-5cf8-57d8-9436-6b5687f8d930
task_key
test--2d572c41-5cf8-57d8-9436-6b5687f8d930
task_revision_id
1
config / split
/ test

Official source

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