# Radius of Convergence Calculator

> Calculate the radius of convergence R of any power series using the Ratio Test with numerical limit approximations.

**URL:** https://www.calculatoranswers.com/radius-of-convergence-calculator
**Category:** Education

## Quick Answer

Compute the radius of convergence R of a power series. Enter the general term to find the range of x-values where the series converges.

## Definition

A radius of convergence calculator is a mathematical utility designed to determine the radius R of a power series, which represents the distance from the center point within which the series converges absolutely. The calculator applies the Ratio Test by evaluating the limit of the absolute ratio of consecutive coefficients as n approaches infinity. It outputs whether the radius is a finite number, zero, or infinite. Students, mathematicians, and physics researchers use this tool to determine the domain of validity for power series expansions and Taylor approximations.

## How to Use

1. **Input the term** — Type the general term of the power series as a function of n into the input box.
2. **Set the center** — Enter the center point value of the expansion, which defaults to zero.
3. **Read the radius** — View the calculated radius of convergence R along with the open interval and limit trend.

## Disclaimer

This calculator provides estimates for educational and planning purposes. Always consult a qualified professional for specific advice on financial, medical, legal, or other regulated decisions.

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