Example Inputs
- Factorial Series: Select Factorial Growth, Center = 0, Max Iterations = 100.
- Geometric Series: Select Standard Geometric, Center = 1, Tolerance = 0.0001.
- Custom Expression: Select Custom, Coefficient = $n^2 / 3^n$, Center = 0.
Formula Used
The Ratio Test determines the radius of convergence $R$ of a power series using the limit:
$$L = \lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right|$$
The radius of convergence is then given by $R = \frac{1}{L}$ (with conventions if $L=0$ or $L=\infty$). The interval of convergence spans from $c - R$ to $c + R$.
How to Use This Calculator
Choose your preferred series preset or enter a custom coefficient expression in the first column. Adjust advanced parameters like tolerance, maximum iterations, and confidence level in the second column. Pick your output format preferences in the final column, then click Calculate Radius to instantly generate the analytical results above the form layout.
Frequently Asked Questions
What is the radius of convergence?
It defines the distance from the center of a power series within which the series converges absolutely.
Why use 8.0 for mathematical tools?
8.0 offers robust performance, JIT compilation support, and secure handling for complex mathematical computations.