Series Convergence Calculator
Determine whether a given series converges or diverges using various tests. Supports geometric, p-series, ratio test, and root test.
Published by:
isCalculator Editorial Team
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How to use this tool?
This calculator determines if an infinite series converges or diverges using common tests.
- Select Series Type from the dropdown (Geometric, P-Series, Ratio Test, or Root Test).
- Enter the required parameters that appear:
- Geometric: Enter the first term (a) and common ratio (r).
- P-Series: Enter the exponent p.
- Ratio/Root Test: Enter the general term using
nas the variable (e.g.,1/factorial(n)or(1+1/n)^n).
- Click "Calculate Convergence".
- View the result (Converges/Diverges/Inconclusive) and step-by-step explanation below.
Tip: For Ratio and Root tests, the calculator approximates the limit using the first 10 terms. Ensure your expression uses n and factorial(n) for factorials.
Previous Results
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Frequently Asked Questions
The ratio test computes the limit of |a_{n+1}/a_n| as n→∞. If the limit < 1, the series converges; if > 1, diverges; if = 1, inconclusive.
A p-series is of the form Σ 1/n^p. It converges if p > 1 and diverges if p ≤ 1.
This calculator supports geometric series, p-series, and general terms via ratio or root test. For other types, results may be approximate.
