Addressing problems in infinite series teaching such as abstract concepts

an emphasis on convergence tests over understanding

and a disconnect between theory and application

this study proposes a reform plan that systematically integrates mathematical experiments into instruction. Based on constructivism and mathematical intuition theory

an experiment-driven teaching model of "problem guidance—experimental exploration—theoretical enhancement—practical application" is designed. Using "using MATLAB

Python

GeoGebra

Mathematica

typical experimental cases for geometric series

harmonic series

and power series are developed

helping students intuitively understand the nature of convergence through numerical computation and visualization. A six-week comparative experiment shows that the experimental class achieved significantly higher chapter test scores than the control class

with notable advantages in conceptual understanding and comprehensive application

and improved learning interest and inquiry skills. The study also identifies problems such as insufficient experimental class hours and disparities in students' software proficiency

and proposes suggestions including building a case library

improving online platforms

and promoting blended teaching

thus providing a practical pathway for the reform of higher mathematics teaching.