e as the Limit of an Infinite Sum — Dynamic Visualization

① This GeoGebra example dynamically demonstrates the natural constant e as the limit of an infinite series, showing how partial sums approach e as n increases. ② The core mathematical concepts are the series definition of e: e = Σ_{k=0}^{∞} 1/k!, and the idea of limits of sequences, involving sequences, limits, and infinite summation. ③ Construction highlights: a slider nSlider controls the number of terms, the Sequence command generates the sequence of reciprocal factorials, the Sum command computes partial sums, Text objects display the current sum and its approximation to e, along with images and explanatory text. Objects used include nSlider, n, text3, text4, text5, E, text6, b, text2, A, pic1, B, list1, a, text1. ④ Suitable for high school to early college mathematics, useful for teaching the series representation of e, limit concepts, and numerical approximation methods, and for classroom demonstrations in calculus or sequence topics.