Series Convergence Test Calculator
Apply common convergence tests to p-series, geometric series, and alternating harmonic-style series.
Calculator
What this calculator teaches
A series is a sum of infinitely many terms.
Convergence tests help decide whether the infinite sum has a finite value.
Formula & Symbols
| Concept | Formula | Meaning |
|---|---|---|
| p-series | Σ1/n^p converges when p>1 | A benchmark for comparison tests. |
| Geometric series | Σarⁿ converges when |r|<1 | Sum equals a/(1-r). |
| Nth-term test | if lim aₙ ≠ 0, series diverges | A quick divergence check. |
Step-by-Step Examples
- Identify it as a p-series with p=2.
- Since p>1, the p-series test says it converges.
Where students use this
Common Mistakes to Avoid
Check denominator, domain, endpoint, and matrix-invertibility conditions before trusting a result.
Carry extra decimals through intermediate steps and round only the final answer.
Some topics need exact symbolic reasoning, while this calculator gives a clear numerical learning check.
Frequently Asked Questions
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Formula Explorer connections
Interpretation: This formula describes an algebraic relationship among variables, functions, equations, roots or sequences. Assumption: Respect the expression’s domain and excluded values. Check roots in the original equation because transformations can introduce extraneous solutions.