Harmonic Sequence and Series: Convergence and Divergence Visualized

This GeoGebra example graphically demonstrates the fundamental properties of the harmonic sequence and series: the harmonic sequence (terms 1/n) converges to 0, while the harmonic series (sum of terms) diverges to infinity. The graph uses point sequences to represent the terms Sn and cumulative sums S1, clearly contrasting the convergence of the sequence with the divergence of the series. Core mathematical concepts include sequence limits, series convergence, divergence of the harmonic series, and partial sums. Construction highlights: using GeoGebra's Sequence command to generate points for sequence terms, Point command to mark key points, with objects including n (term index), Sn (nth term), S1 (partial sum), and auxiliary points A and B, allowing dynamic adjustment of n to observe trends. Suitable for high school and above when learning sequences and series, and for introductory calculus in university, helping students intuitively grasp the difference between convergence and divergence.