# Infinite Series Calculator

> Test an infinite geometric series for convergence and find the sum when |r| < 1 using S = a / (1 − r). Returns the sum, the convergence verdict, and a preview of the first few terms.

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

## Quick Answer

Calculate the sum and convergence of infinite series. Enter the formula and variable parameters to determine convergence limits and values.

## Definition

An infinite series calculator is an advanced mathematics tool that evaluates the behavior of a sequence summed to infinity. The calculator analyzes the terms of the series and applies standard calculus tests, including the geometric series test, ratio test, integral test, and p-series test, to determine if the summation converges to a finite value or diverges. For convergent geometric or telescoping series, it computes the exact sum to infinity. Calculus students and mathematicians use this tool to verify series convergence behavior.

## How to Use

1. **Enter series formula** — Type the algebraic expression representing the terms of your infinite series.
2. **Set starting index** — Input the starting value of the summation variable, typically zero or one.
3. **Read convergence analysis** — View the convergence status, the calculus tests applied, and the calculated sum if convergent.

## 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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