Where Series Work

Radius of convergence

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A series converges only within its radius of convergence.
• The radius reaches out to the nearest problem point, possibly a complex one.
• $e^x$, $\sin x$ and $\cos x$ converge everywhere.

Steps

1. A familiar series
2. Partial sums that explode
3. Inside the radius
4. What’s the obstacle?
5. Another radius
6. A hidden obstacle