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.