{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"omni-math","formal_name":"Omni-MATH","introduction":"Omni-MATH evaluates mathematical reasoning on Olympiad-level problems. Its official dataset contains 4,428 problems accompanied by domain and difficulty information.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"232b0f2d-e844-5bea-96aa-f3ebf1ba57b4","task_key":"test--232b0f2d-e844-5bea-96aa-f3ebf1ba57b4","task_revision_id":"1","upstream_id":"","short_description":"For all $n \\geq 1$, let \\[ a_n = \\sum_{k=1}^{n-1} \\frac{\\sin \\left(…","config":"","split":"test","body":"{\"problem\":\"For all $n \\\\geq 1$, let \\\\[ a_n = \\\\sum_{k=1}^{n-1} \\\\frac{\\\\sin \\\\left( \\\\frac{(2k-1)\\\\pi}{2n} \\\\right)}{\\\\cos^2 \\\\left( \\\\frac{(k-1)\\\\pi}{2n} \\\\right) \\\\cos^2 \\\\left( \\\\frac{k\\\\pi}{2n} \\\\right)}. \\\\] Determine \\\\[ \\\\lim_{n \\\\to \\\\infty} \\\\frac{a_n}{n^3}. \\\\]\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}