Canonical URI: https://w3id.org/kmath/textbook_solution/chunjae_jeon_solution_p156_p111_competency_pascal_identity
| rdf:type | math:TextbookSolution |
|---|---|
| rdfs:label | 천재전 p156 해설 - p111 역량 키우기 |
| rdfs:comment | 천재전 공통수학1 정답과 해설 p156의 p111 역량 키우기 조합 항등식 증명 풀이 원문. |
| math:answerText | \({}_nC_r={}_{n-1}C_{r-1}+{}_{n-1}C_r\) |
| math:explanationText | \[ {}_{n-1}C_{r-1}+{}_{n-1}C_r =\frac{(n-1)!}{(r-1)!(n-r)!}+\frac{(n-1)!}{r!(n-r-1)!} \] \[ =\frac{(n-1)!\,r+(n-1)!(n-r)}{r!(n-r)!} \] \[ =\frac{n\times(n-1)!}{r!(n-r)!} =\frac{n!}{r!(n-r)!} ={}_nC_r \] |
| math:hasFigure | problem_figure:chunjae_jeon_p111_pascal_identity_comic |
| math:mappingConfidence | 1.0 |
| math:pageStart | 156 |
| math:problem | textbook_problem:chunjae_jeon_vision_p111_competency_pascal_identity |
| math:reviewStatus | reviewed |
| math:solutionKind | worked_solution |
| math:usesSolutionPattern | solution_pattern:combination_pascal_identity |