# Convergence Calculator

> Test any infinite series for convergence or divergence using the Ratio Test, Root Test, and partial sum stabilization heuristics.

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

## Quick Answer

Determine if an infinite series converges or diverges. Enter the general term a_n and choose a test to view the limit conclusion.

## Definition

A convergence calculator is an educational utility that tests infinite numerical series to determine if they converge or diverge. It supports several classical tests, including the Ratio Test and Root Test, by calculating their limits at large indices. In auto mode, the calculator tries multiple tests sequentially and falls back to a numerical partial sum stabilization check to simulate Comparison and Integral Tests. Students and educators use this solver to analyze series convergence behaviors and verify homework calculations with step-by-step limits.

## How to Use

1. **Enter the general term** — Type the expression of the general term a_n of the series in the input.
2. **Choose the test** — Select a specific convergence test from the options or choose auto mode.
3. **Analyze the results** — Read the convergence conclusion along with the limit value and worked explanation.

## 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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