Convergence Calculator
Determine if a series converges or diverges using the ratio test, root test, or comparison test. Supports common series types.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the Convergence Calculator
This tool determines whether an infinite series converges or diverges. Follow these steps:
- Select Series Type – Choose from p-Series, Geometric, or General (ratio test).
- Enter Parameters:
- p-Series: Enter a positive number for p (e.g., 2). The series is 1/np.
- Geometric: Enter the first term a (any number) and common ratio r (e.g., 0.5).
- General: Type the general term using
nas the variable (e.g.,1/n^2). Supports factorial (!) and exponential patterns.
- Click "Calculate Convergence" – The result shows Converges or Diverges with a brief explanation.
Note: For the general term, the calculator uses simple heuristics. For accurate results with complex series, use a more rigorous test.
Previous Results
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Frequently Asked Questions
A convergence calculator helps determine whether an infinite series converges or diverges based on mathematical tests like the ratio test, root test, or comparison test.
This calculator supports p-series (1/n^p), geometric series (a*r^n), and general series using the ratio test with a user-defined term.
The ratio test is a powerful tool, but for complex terms, manual verification is recommended. Our calculator uses heuristics for common patterns.
