---
title: "Radius of Convergence — AP Calc BC Definition & Exam Guide"
description: "The radius of convergence is the distance from a power series' center within which the series converges. Learn how the ratio test finds it for AP Calc BC Unit 10."
canonical: "https://fiveable.me/ap-calc/key-terms/radius-of-convergence"
type: "key-term"
subject: "AP Calculus AB/BC"
---

# Radius of Convergence — AP Calc BC Definition & Exam Guide

## Definition

The radius of convergence refers to the distance from the center of a power series to the nearest point where the series converges. If the radius of convergence is 0, it means that the power series only converges at its center and nowhere else.

## Review

### Related Terms

- [Interval of Convergence](/ap-calc/key-terms/interval-of-convergence): The range of x-values for which a power series converges.
- Center of Convergence: The point about which a power series expands.
- Divergence Test: A method used to determine if a given sequence or series diverges.