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Omni-MATH / Given a positive integer n, let M(n) be the largest integer m such that binom{m}{n-1} > binom{m-1}{n}. Evaluate lim_(n→∞)(M(n))/(n).

Problem

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problem

Given a positive integer nn, let M(n)M(n) be the largest integer mm such that \[ \binom{m}{n-1} > \binom{m-1}{n}. \] Evaluate limn→∞M(n)n. \lim_{n \to \infty} \frac{M(n)}{n}.
Plain-text mathematical notation (without MathML)
Given a positive integer n, let M(n) be the largest integer m such that \[ \binom{m}{n-1} > \binom{m-1}{n}. \] Evaluate lim_(n→∞)(M(n))/(n).
Original LaTeX notation
Given a positive integer $n$, let $M(n)$ be the largest integer $m$ such that \[ \binom{m}{n-1} > \binom{m-1}{n}. \] Evaluate \[ \lim_{n \to \infty} \frac{M(n)}{n}. \]

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Source and history

task_id
0df4a414-9e25-560f-88d1-6b6ea6edc3e2
task_key
test--0df4a414-9e25-560f-88d1-6b6ea6edc3e2
task_revision_id
1
config / split
/ test

Official source

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