{"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":"8a6f9afa-63f7-585e-aa27-287ec1a3f6f2","task_key":"test--8a6f9afa-63f7-585e-aa27-287ec1a3f6f2","task_revision_id":"1","upstream_id":"","short_description":"The sequences of real numbers $\\left\\{a_{i}\\right\\}_{i=1}^{\\infty}$ and…","config":"","split":"test","body":"{\"problem\":\"The sequences of real numbers $\\\\left\\\\{a_{i}\\\\right\\\\}_{i=1}^{\\\\infty}$ and $\\\\left\\\\{b_{i}\\\\right\\\\}_{i=1}^{\\\\infty}$ satisfy $a_{n+1}=\\\\left(a_{n-1}-1\\\\right)\\\\left(b_{n}+1\\\\right)$ and $b_{n+1}=a_{n} b_{n-1}-1$ for $n \\\\geq 2$, with $a_{1}=a_{2}=2015$ and $b_{1}=b_{2}=2013$. Evaluate, with proof, the infinite sum $\\\\sum_{n=1}^{\\\\infty} b_{n}\\\\left(\\\\frac{1}{a_{n+1}}-\\\\frac{1}{a_{n+3}}\\\\right)$.\"}","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":[]}