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Omni-MATH / Choose positive integers b_1, b_2, dotsc satisfying
Problem
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problem
Choose positive integers
$b_1, b_2, \dotsc$ satisfying
\[1=\frac{b_1}{1^2} > \frac{b_2}{2^2} > \frac{b_3}{3^2} > \frac{b_4}{4^2} > \dotsb\]
and let denote the largest real number satisfying for all positive integers . What are the possible values of across all possible choices of the sequence ?
[i]Carl Schildkraut and Milan Haiman[/i]Plain-text mathematical notation (without MathML)
Choose positive integers $b_1, b_2, \dotsc$ satisfying
\[1=\frac{b_1}{1^2} > \frac{b_2}{2^2} > \frac{b_3}{3^2} > \frac{b_4}{4^2} > \dotsb\]
and let r denote the largest real number satisfying (b_(n))/(n²)≥r for all positive integers n. What are the possible values of r across all possible choices of the sequence (b_(n))?
[i]Carl Schildkraut and Milan Haiman[/i]Original LaTeX notation
Choose positive integers $b_1, b_2, \dotsc$ satisfying
\[1=\frac{b_1}{1^2} > \frac{b_2}{2^2} > \frac{b_3}{3^2} > \frac{b_4}{4^2} > \dotsb\]
and let $r$ denote the largest real number satisfying $\tfrac{b_n}{n^2} \geq r$ for all positive integers $n$. What are the possible values of $r$ across all possible choices of the sequence $(b_n)$?
[i]Carl Schildkraut and Milan Haiman[/i]Discussion
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