Quick guide
How to use this calculator
- Choose the supported sequence, series, or analysis mode when the page offers one.
- Enter the labelled parameters or comma-separated finite terms.
- Read the primary result, then use the supporting classification, formula, or generated values.
Calculation method
Apply the stated sequence or series rule
Geometric Σa₁rⁿ=a₁/(1−r) for |r|<1; p-series converges iff p>1.
The calculator validates the selected family and its mathematical domain before returning a result.
Worked example
Worked example
A geometric series with first term 1 and ratio 1/2 sums to 2.
Geometric Σa₁rⁿ=a₁/(1−r) for |r|<1; p-series converges iff p>1.
Supported inputs
Precision and limits
Supported scope
General-looking pages use explicitly listed families instead of pretending to parse or prove arbitrary symbolic sequences and series.
Numerical precision
Fibonacci, Lucas, Tribonacci, Pascal, and triangular-number outputs use exact integers. Analytical and decimal calculations use finite double-precision arithmetic and normally display 12 significant digits.
Visible computational limits
Named-sequence indices are limited to 0–5000; Pascal rows to 0–200; harmonic indices to 1–1,000,000; recurrence and arithmetic-geometric generation to 1000; Taylor degree to 100; Lagrange degree to 170; sigma bounds to −100,000…100,000 with at most 200,000 steps; pattern and difference lists to 100 and 50 terms. Field labels show narrower limits where applicable.
Convergence
A convergence test applies only when its hypotheses match the entered series. Inconclusive tests and power-series endpoints are reported honestly rather than guessed.