Use this radius of convergence calculator to quickly determine the radius within which a given power series converges to a function.

## Radius of Convergence Calculator

Enter the coefficients of the power series:

## How to Use the Calculator

Enter the coefficients of the power series (a_n) terms separated by commas in the input field and press the “Calculate” button. The radius of convergence is the distance within which the power series converges.

## How It Calculates the Results

This calculator uses the formula based on the ratio test for convergence of infinite series. If lim |aₙ/aₙ₊₁| exists as n approaches infinity, the radius of convergence (R) is equal to this limit. The calculator computes R for a finite set of coefficients to approximate the radius.

## Limitations

The calculator is intended for educational purposes and is not foolproof. It assumes that the coefficients entered are for a power series centered at zero and that the user provides a sufficiently large number of terms for an accurate approximation. It does not handle cases where the ratio does not stabilize or the series has non-numeric terms. For best results, enter a sequence of coefficients that represents the beginning of an infinite series.