# Interval of Convergence Calculator

> Find the interval of convergence of a power series including endpoint convergence testing using partial sum heuristics.

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

## Quick Answer

Find the complete interval of convergence for a power series, including boundary endpoints. Enter the general term and center point to compute the bracketed interval.

## Definition

An interval of convergence calculator is a calculus tool that determines the full set of real numbers for which a power series converges. It first computes the radius of convergence using the Ratio Test and then evaluates the behavior of the series at the boundary endpoints by substituting their values into the general term. By evaluating the stabilization of numerical partial sums up to one thousand terms, the tool decides whether each endpoint converges or diverges. Students use this calculator to identify if intervals are open, closed, or half-open.

## How to Use

1. **Enter the term** — Type the general term of the power series including the variables x and n.
2. **Define the center** — Specify the expansion center point value of the power series.
3. **Review endpoint tests** — Check the numerical convergence results and partial sums at both boundary endpoints.
4. **Read the interval** — View the final bracketed interval of convergence representing all valid x-values.

## 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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