Taylor Series Visualization for 1/(1-x) and Partial-Sum Approximation

This example visualizes how the function f(x)=1/(1-x) is approximated by Taylor (power) series partial sums of different orders, showing the convergence behavior within the radius of convergence and the truncation error when the series is cut off. The main mathematical ideas are Taylor/power series expansion, the geometric-series structure of 1/(1-x), and the concept of partial sums approaching the original function. In GeoGebra, the construction centers on the command “Sum” to compute the first n terms of the series and build a polynomial approximation for comparison. The involved objects “f, n, g, a, text2” correspond to the target function, the adjustable order parameter n, auxiliary expression(s) for the series approximation, the variable or evaluation point a, and text labeling (e.g., displaying formulas/parameters via text2). Suitable for high-school advanced study through calculus or mathematical analysis instruction, and for learning function approximation via series.