本研究以数学史与数学教育（HPM）视角为指导，聚焦高中数学等比数列求和公式教学。通过设计与实施HPM视角的教学案例，展示了等比数列的历史演变、原理发现与证实过程，成功将数学史融入教学，提升学生学习兴趣、理解深度与核心素养。教学中运用错位相减法与提取公比法推导公式，解决实际问题，展示了公式在现实生活中的应用价值。问卷调查结果显示学生高度认可数学史在提高学习兴趣与理解能力的作用，但实际教学中数学史的广泛应用程度有限。实证研究与案例分析揭示了数学史在等比数列教学中的重要意义与实际价值，对学生情感态度与价值观产生积极影响。本研究为教师提供了HPM教学实践案例，为数学史与数学教育深度融合的研究与实践提供了理论与实践参考。研究虽取得一定成果，但受限于单一案例、未全面考虑教学风格与学生差异等因素，未来研究需扩大样本、深化理论与实践融合，以推动数学史在数学教育中的应用与推广。

This study is guided by the perspective of History and Pedagogy of Mathematics (HPM) and focuses on the teaching of the sum formula for geometric series in high school mathematics. Through the design and implementation of an HPM-informed instructional case, it presents the historical evolution, principle discovery, and verification process of geometric sequences, effectively integrating mathematical history into instruction to enhance students' learning interest, depth of understanding, and core competencies. In the teaching, the formula is derived using the methods of telescoping and extracting the common ratio, and applied to solve real-world problems, thereby demonstrating the practical value of the formula in everyday life. The results of a questionnaire survey indicate that students strongly acknowledge the role of mathematical history in boosting their learning interest and comprehension abilities, yet its widespread application in actual teaching remains limited. Empirical research and case analysis reveal the significant importance and practical value of mathematical history in the teaching of geometric sequences, exerting a positive influence on students' affective attitudes and values. This study furnishes teachers with an HPM-based instructional practice case and provides theoretical and practical reference for further research and implementation that deeply integrate mathematical history and education. Despite achieving certain outcomes, the study is constrained by its reliance on a single case and failure to fully account for teaching styles and student differences. Future research should expand the sample size, deepen the fusion of theory and practice, and thus advance the application and promotion of mathematical history within mathematics education.