Which test should I use for a factorial series?

The Ratio Test is usually best for series involving factorials or exponentials, because the factorials cancel nicely when you compute a_{n+1}/a_n.

What does "Inconclusive" mean?

The chosen test cannot determine convergence for the given input (e.g. Ratio Test with L = 1). You need to apply a different test.

Can a series pass the Ratio Test at L = 1 and still converge?

Yes — when L = 1 the Ratio Test gives no information. The p-series 1/n^2 converges but its ratio limit equals 1.

What is the difference between absolute and conditional convergence?

A series converges absolutely if the series of absolute values converges. Conditional convergence means the original series converges but not absolutely (common with alternating series by the AST).

Does the Integral Test require a specific kind of function?

Yes — the function f(x) corresponding to your series must be continuous, positive, and decreasing on [1, ∞) for the Integral Test to apply.

How do I use the Comparison Test?

Find a known series b_n that is larger (for divergence) or smaller (for convergence) than your series a_n term-by-term, then enter the limit L = lim(a_n / b_n). If 0 < L < ∞ both series share the same fate (Limit Comparison).

Convergence Test Helper

Name: Convergence Test Helper
Availability: InStock
Author: Nham Vu

Select a convergence test, enter your series parameters, and get a step-by-step verdict — converges, diverges, or inconclusive.

Select a Convergence Test

Select a test above to enter parameters.

Choose a test on the left, enter the parameters, and click Run Test.

Summary