Ratio Test Calculator

Test series convergence using the ratio test.

How It Works

  1. Enter limit L. Type L = lim |aₙ₊₁/aₙ| or use a preset series term below.
  2. Define aₙ. Enter the general term using n (e.g. 2ⁿ/n!) in the Series Term Analyzer.
  3. Apply the ratio test. If L < 1 the series converges; if L > 1 it diverges; if L = 1 the test is inconclusive.
  4. Read step-by-step solution. See the full decision path with computed L value.
  5. Compare other tests. Check root test and nth-term test hints when L = 1.

Pair with our Fraction Calculator or Math Calculators.

Enter values to see results.

Formula & Reference

L < 1 converges · L > 1 diverges · L = 1 inconclusive