Geometric Series: Partial Sums in the Plane Lesson 3
Drag z and watch the partial sums of Σzⁿ trace a path: a spiral forced inward to 1/(1−z) when |z| < 1, an unbounded outward spiral when |z| > 1, and endless circling right on the boundary. An ε-disk around the limit makes the ε–N definition of convergence literal — find the N past which the path never leaves.